Maharashtra State BoardHSC Science (General) 11th
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Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board chapter 6 - Functions [Latest edition]

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Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board - Shaalaa.com
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Chapter 6: Functions

Exercise 6.1Exercise 6.2Miscellaneous Exercise 6
Exercise 6.1 [Pages 117 - 119]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 6 Functions Exercise 6.1 [Pages 117 - 119]

Exercise 6.1 | Q 1. (a) | Page 117

Check if the following relation is a function.

Exercise 6.1 | Q 1. (b) | Page 117

Check if the following relation is a function.

Exercise 6.1 | Q 1. (c) | Page 118

Check if the following relation is a function.

Exercise 6.1 | Q 2. (a) | Page 118

Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.

{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}

Exercise 6.1 | Q 2. (b) | Page 118

Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.

{(1, 2), (2, −1), (3, 1), (4, 3)}

Exercise 6.1 | Q 2. (c) | Page 118

Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.

{(1, 3), (4, 1), (2, 2)}

Exercise 6.1 | Q 2. (d) | Page 118

Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.

{(1, 1), (2, 1), (3, 1), (4, 1)}

Exercise 6.1 | Q 3. (a) | Page 118

Check if the relation given by the equation represents y as function of x:

2x + 3y = 12

Exercise 6.1 | Q 3. (b) | Page 118

Check if the relation given by the equation represents y as function of x:

x + y2 = 9

Exercise 6.1 | Q 3. (c) | Page 118

Check if the relation given by the equation represents y as function of x:

x2 − y = 25

Exercise 6.1 | Q 3. (d) | Page 118

Check if the relation given by the equation represents y as function of x:

2y + 10 = 0

Exercise 6.1 | Q 3. (e) | Page 118

Check if the relation given by the equation represents y as function of x:

3x − 6 = 21

Exercise 6.1 | Q 4. (a) | Page 118

If f(m) = m2 − 3m + 1, find f(0)

Exercise 6.1 | Q 4. (b) | Page 118

If f(m) = m2 − 3m + 1, find f(−3)

Exercise 6.1 | Q 4. (c) | Page 118

If f(m) = m2 − 3m + 1, find `f(1/2)`

Exercise 6.1 | Q 4. (d) | Page 118

If f(m) = m2 − 3m + 1, find f(x + 1)

Exercise 6.1 | Q 4. (e) | Page 118

If f(m) = m2 − 3m + 1, find f(− x)

Exercise 6.1 | Q 4. (f) | Page 118

If f(m) = m2 − 3m + 1, find `(("f"(2 + "h") - "f"(2))/"h"), "h" ≠ 0`

Exercise 6.1 | Q 5. (a) | Page 118

Find x, if g(x) = 0 where g(x) = `(5x - 6)/7`

Exercise 6.1 | Q 5. (b) | Page 118

Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`

Exercise 6.1 | Q 5. (c) | Page 118

Find x, if g(x) = 0 where g(x) = 6x2 + x − 2

Exercise 6.1 | Q 5. (d) | Page 118

Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6

Exercise 6.1 | Q 6. (a) | Page 118

Find x, if f(x) = g(x) where f(x) = x4 + 2x2, g(x) = 11x2

Exercise 6.1 | Q 6. (b) | Page 118

Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x

Exercise 6.1 | Q 7 | Page 118

If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b

Exercise 6.1 | Q 8. (a) | Page 118

Find the domain and range of the following function.

f(x) = 7x2 + 4x − 1

Exercise 6.1 | Q 8. (b) | Page 118

Find the domain and range of the following function.

g(x) = `(x + 4)/(x - 2)`

Exercise 6.1 | Q 8. (c) | Page 118

Find the domain and range of the follwoing function.

h(x) = `sqrt(x + 5)/(5 + x)`

Exercise 6.1 | Q 8. (d) | Page 118

Find the domain and range of the following function.

f(x) = `root(3)(x + 1)`

Exercise 6.1 | Q 8. (e) | Page 118

Find the domain and range of the following function.

f(x) = `sqrt((x - 2)(5 - x)`

Exercise 6.1 | Q 8. (f) | Page 118

Find the domain and range of the following function.

f(x) = `sqrt((x - 3)/(7 - x))`

Exercise 6.1 | Q 8. (g) | Page 118

Find the domain and range of the following function.

f(x) = `sqrt(16 - x^2)`

Exercise 6.1 | Q 9. (a) | Page 118

Express the area A of a square as a function of its side s

Exercise 6.1 | Q 9. (b) | Page 118

Express the area A of a square as a function of its perimeter P

Exercise 6.1 | Q 10. (a) | Page 118

Express the area A of circle as a function of its radius r

Exercise 6.1 | Q 10. (b) | Page 118

Express the area A of circle as a function of its diameter d

Exercise 6.1 | Q 10. (c) | Page 118

Express the area A of circle as a function of its circumference C.

Exercise 6.1 | Q 11 | Page 118

An open box is made from a square of cardboard of 30 cms side, by cutting squares of length x centimeters from each corner and folding the sides up. Express the volume of the box as a function of x. Also find its domain

Exercise 6.1 | Q 12 | Page 118

Let f be a subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z? Justify?

Exercise 6.1 | Q 13. (a) | Page 118

Check the injectivity and surjectivity of the following function.

f : N → N given by f(x) = x2 

Exercise 6.1 | Q 13. (b) | Page 118

Check the injectivity and surjectivity of the following function.

f : Z → Z given by f(x) = x2 

Exercise 6.1 | Q 13. (c) | Page 118

Check the injectivity and surjectivity of the following function.

f : R → R given by f(x) = x2 

Exercise 6.1 | Q 13. (d) | Page 119

Check the injectivity and surjectivity of the following function.

f : N → N given by f(x) = x3

Exercise 6.1 | Q 13. (e) | Page 119

Check the injectivity and surjectivity of the following function.

f : R → R given by f(x) = x3 

Exercise 6.1 | Q 14 | Page 119

Show that if f : A → B and g : B → C are one-one, then g ° f is also one-one

Exercise 6.1 | Q 15 | Page 119

Show that if f : A → B and g : B → C are onto, then g ° f is also onto

Exercise 6.1 | Q 16 | Page 119

lf f(x) = 3(4x+1), find f(– 3)

Exercise 6.1 | Q 17. (a) | Page 119

Express the following exponential equation in logarithmic form

25 = 32

Exercise 6.1 | Q 17. (b) | Page 119

Express the following exponential equation in logarithmic form

54° = 1

Exercise 6.1 | Q 17. (c) | Page 119

Express the following exponential equation in logarithmic form

231 = 23

Exercise 6.1 | Q 17. (d) | Page 119

Express the following exponential equation in logarithmic form

`9^(3/2)` = 27

Exercise 6.1 | Q 17. (e) | Page 119

Express the following exponential equation in logarithmic form

3–4 = `1/81`

Exercise 6.1 | Q 17. (f) | Page 119

Express the following exponential equation in logarithmic form

10−2 = 0.01

Exercise 6.1 | Q 17. (g) | Page 119

Express the following exponential equation in logarithmic form

e2 = 7.3890

Exercise 6.1 | Q 17. (h) | Page 119

Express the following exponential equation in logarithmic form

`"e"^(1/2)` = 1.6487

Exercise 6.1 | Q 17. (i) | Page 119

Express the following exponential equation in logarithmic form

e–x = 6

Exercise 6.1 | Q 18. (a) | Page 119

Express the following logarithmic equation in exponential form

log2 64 = 6

Exercise 6.1 | Q 18. (b) | Page 119

Express the following logarithmic equation in exponential form

`log_5  1/25` = – 2

Exercise 6.1 | Q 18. (c) | Page 119

Express the following logarithmic equation in exponential form

log10 (0.001) = −3

Exercise 6.1 | Q 18. (d) | Page 119

Express the following logarithmic equation in exponential form

`log_(1/2) (8)` = – 3

Exercise 6.1 | Q 18. (e) | Page 119

Express the following logarithmic equation in exponential form

ln 1 = 0

Exercise 6.1 | Q 18. (f) | Page 119

Express the following logarithmic equation in exponential form

ln e = 1

Exercise 6.1 | Q 18. (g) | Page 119

Express the following logarithmic equation in exponential form

In `1/2` = – 0.693

Exercise 6.1 | Q 19. (a) | Page 119

Find the domain of f(x) = ln (x − 5)

Exercise 6.1 | Q 19. (b) | Page 119

Find the domain of f(x) = log10 (x2 − 5x + 6)

Exercise 6.1 | Q 20. (a) | Page 119

Write the following expression as sum or difference of logarithm

`log ("pq"/"rs")`

Exercise 6.1 | Q 20. (b) | Page 119

Write the following expression as sum or difference of logarithm

`log (sqrt(x) root(3)(y))`

Exercise 6.1 | Q 20. (c) | Page 119

Write the following expression as sum or difference of logarithm

In `(("a"^3 ("a" - 2)^2)/sqrt("b"^2 + 5))`

Exercise 6.1 | Q 20. (d) | Page 119

Write the following expression as sum or difference of logarithm

In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`

Exercise 6.1 | Q 21. (a) | Page 119

Write the following expression as a single logarithm.

5 log x + 7 log y − log z

Exercise 6.1 | Q 21. (b) | Page 119

Write the following expression as a single logarithm.

`1/3 log (x - 1) + 1/2 log (x)`

Exercise 6.1 | Q 21. (c) | Page 119

Write the following expression as a single logarithm.

ln (x + 2) + ln (x − 2) − 3 ln (x + 5)

Exercise 6.1 | Q 22 | Page 119

Given that log 2 = a and log 3 = b, write `log sqrt(96)` in terms of a and b

Exercise 6.1 | Q 23. (a) | Page 119

Prove that `"b"^(log_"b""a"` = a

Exercise 6.1 | Q 23. (b) | Page 119

Prove that logbm a = `1/"m" log_"b""a"`

Exercise 6.1 | Q 23. (c) | Page 119

Prove that alogcb = blogca

Exercise 6.1 | Q 24 | Page 119

If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b

Exercise 6.1 | Q 25. (a) | Page 119

Solve for x.

log2 + log(x + 3) – log(3x – 5) = log3

Exercise 6.1 | Q 25. (b) | Page 119

Solve for x.

2 log10 x = `1 + log_10 (x + 11/10)`

Exercise 6.1 | Q 25. (c) | Page 119

Solve for x.

log2 x + log4 x + log16 x = `21/4`

Exercise 6.1 | Q 25. (d) | Page 119

Solve for x.

x + log10 (1 + 2x) = x log10 5 + log10 6

Exercise 6.1 | Q 26 | Page 119

If `log((x + y)/3) = 1/2 log x + 1/2 logy`, show that `x/y + y/x` = 7

Exercise 6.1 | Q 27 | Page 119

If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy 

Exercise 6.1 | Q 28 | Page 119

If x = loga bc, y = logb ca, z = logc ab then prove that `1/(1 + x) + 1/(1 + y) + 1/(1 + z)` = 1

Exercise 6.2 [Pages 127 - 128]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 6 Functions Exercise 6.2 [Pages 127 - 128]

Exercise 6.2 | Q 1. (a) | Page 127

If f(x) = 3x + 5, g(x) = 6x − 1, then find (f + g) (x)

Exercise 6.2 | Q 1. (b) | Page 127

If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)

Exercise 6.2 | Q 1. (c) | Page 127

If f(x) = 3x + 5, g(x) = 6x − 1, then find (fg) (3)

Exercise 6.2 | Q 1. (d) | Page 127

If f(x) = 3x + 5, g(x) = 6x − 1, then find `("f"/"g") (x)` and its domain

Exercise 6.2 | Q 2 | Page 127

Let f : {2, 4, 5} → {2, 3, 6} and g : {2, 3, 6} → {2, 4} be given by f = {(2, 3), (4, 6), (5, 2)} and g = {(2, 4), (3, 4), (6, 2)}. Write down g ° f

Exercise 6.2 | Q 3. (a) | Page 127

If f(x) = 2x2 + 3, g (x) = 5x − 2, then find f ° g

Exercise 6.2 | Q 3. (b) | Page 127

If f(x) = 2x2 + 3, g(x) = 5x − 2, then find g ° f

Exercise 6.2 | Q 3. (c) | Page 127

If f(x) = 2x2 + 3, g(x) = 5x − 2, then find f ° f

Exercise 6.2 | Q 3. (d) | Page 127

If f(x) = 2x2 + 3, g (x) = 5x − 2, then find g ° g

Exercise 6.2 | Q 4. (a) | Page 127

Verify that f and g are inverse functions of each other, where f(x) = `(x - 7)/4`, g(x) = 4x + 7

Exercise 6.2 | Q 4. (b) | Page 127

Verify that f and g are inverse functions of each other, where f(x) = x3 + 4, g(x) = `root(3)(x - 4)`

Exercise 6.2 | Q 4. (c) | Page 127

Verify that f and g are inverse functions of each other, where f(x) = `(x + 3)/(x - 2)`, g(x) = `(2x + 3)/(x - 1)`

Exercise 6.2 | Q 5. (a) | Page 128

Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = 5x2

Exercise 6.2 | Q 5. (b) | Page 128

Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = 8

Exercise 6.2 | Q 5. (c) | Page 128

Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = `(6x - 7)/3`

Exercise 6.2 | Q 5. (d) | Page 128

Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = `sqrt(4x + 5)`

Exercise 6.2 | Q 5. (e) | Page 128

Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = 9x3 + 8

Exercise 6.2 | Q 5. (f) | Page 128

Check if the following function has an inverse function. If yes, find the inverse function.

f(x) = `{(x + 7, x < 0),(8 - x, x ≥ 0):}`

Exercise 6.2 | Q 6. (a) | Page 128

If f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`, then find f(3)

Exercise 6.2 | Q 6. (b) | Page 128

If f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`, then find f(2)

Exercise 6.2 | Q 6. (c) | Page 128

If f(x) = `{(x^2 + 3, x ≤ 2),(5x + 7, x > 2):}`, then find f(0)

Exercise 6.2 | Q 7. (a) | Page 128

If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(– 4)

Exercise 6.2 | Q 7. (b) | Page 128

If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(– 3)

Exercise 6.2 | Q 7. (c) | Page 128

If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(1)

Exercise 6.2 | Q 7. (d) | Page 128

If f(x) = `{(4x - 2",", x ≤ -3),(5",", -3 < x < 3),(x^2",", x ≥ 3):}`, then find f(5)

Exercise 6.2 | Q 8. (a) | Page 128

If f(x) = 2|x| + 3x, then find f(2)

Exercise 6.2 | Q 8. (b) | Page 128

If f(x) = 2|x| + 3x, then find f(– 5)

Exercise 6.2 | Q 9. (a) | Page 128

If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(7.2)

Exercise 6.2 | Q 9. (b) | Page 128

If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(0.5)

Exercise 6.2 | Q 9. (c) | Page 128

If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find `"f"(- 5/2)`

Exercise 6.2 | Q 9. (d) | Page 128

If f(x) = 4[x] − 3, where [x] is greatest integer function of x, then find f(2π), where π = 3.14

Exercise 6.2 | Q 10. (a) | Page 128

If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 1)

Exercise 6.2 | Q 10. (b) | Page 128

If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find `"f"(1/4)`

Exercise 6.2 | Q 10. (c) | Page 128

If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 1.2)

Exercise 6.2 | Q 10. (d) | Page 128

If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find f(– 6)

Exercise 6.2 | Q 11. (a) | Page 128

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

|x + 4| ≥ 5

Exercise 6.2 | Q 11. (b) | Page 128

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

|x − 4| + |x − 2| = 3

Exercise 6.2 | Q 11. (c) | Page 128

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

x2 + 7 |x| + 12 = 0

Exercise 6.2 | Q 11. (d) | Page 128

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

|x| ≤ 3

Exercise 6.2 | Q 11. (e) | Page 128

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

2|x| = 5

Exercise 6.2 | Q 11. (f) | Page 128

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

[x + [x + [x]]] = 9

Exercise 6.2 | Q 11. (g) | Page 128

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

{x} > 4

Exercise 6.2 | Q 11. (h) | Page 128

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

{x} = 0

Exercise 6.2 | Q 11. (i) | Page 128

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

{x} = 0.5

Exercise 6.2 | Q 11. (j) | Page 128

Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.

2{x} = x + [x]

Miscellaneous Exercise 6 [Pages 129 - 130]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 6 Functions Miscellaneous Exercise 6 [Pages 129 - 130]

Miscellaneous Exercise 6 | Q I. (1) | Page 129

Select the correct answer from given alternatives.

If log (5x – 9) – log (x + 3) = log 2 then x = ...............

  • 3

  • 5

  • 2

  • 7

Miscellaneous Exercise 6 | Q I. (2) | Page 129

Select the correct answer from given alternatives.

If log10(log10(log10x)) = 0 then x =

  • 1000

  • 1010 

  • 10

  • 0

Miscellaneous Exercise 6 | Q I. (3) | Page 129

Select the correct answer from given alternatives.

Find x, if 2log2 x = 4

  • 4, −4

  • 4

  • −4

  • not defined

Miscellaneous Exercise 6 | Q I. (4) | Page 129

Select the correct answer from given alternatives.

The equation logx2 16 + log2x 64 = 3 has,

  • one irrational solution

  • no prime solution

  • two real solutions

  • one integral solution

Miscellaneous Exercise 6 | Q I. (5) | Page 129

Select the correct answer from given alternatives.

If f(x) =`1/(1 - x)`, then f{f[f(x)]} is

  • x – 1

  • 1 – x

  • x

  • – x

Miscellaneous Exercise 6 | Q I. (6) | Page 130

Select the correct answer from given alternatives.

If f : R → R is defined by f(x) = x3 then f–1 (8) is equal to :

  • {2}

  • {–2, 2}

  • {–2}

  • (–2, 2)

Miscellaneous Exercise 6 | Q I. (7) | Page 130

Select the correct answer from given alternatives.

Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is ______.

  • `(x - 1)/(3x + 2)`

  • `(x + 1)/(3x - 2)`

  • `(2x + 1)/(1 - 3x)`

  • `(3x + 2)/(x - 1)`

Miscellaneous Exercise 6 | Q I. (8) | Page 130

Select the correct answer from given alternatives

If f(x) = 2x2 + bx + c and f(0) = 3 and f(2) = 1, then f(1) is equal to

  • –2

  • 0

  • 1

  • 2

Miscellaneous Exercise 6 | Q I. (9) | Page 130

Select the correct answer from given alternatives

The domain of `1/([x] - x)` where [x] is greatest integer function is

  • R

  • Z

  • R − Z

  • Q - {o}

Miscellaneous Exercise 6 | Q I. (10) | Page 130

Select the correct answer from given alternative.

The domain and range of f(x) = 2 − |x − 5| is

  • R+, `(- ∞, 1]`

  • R, `(- ∞, 2]`

  • R, `(- ∞, 2)`

  • R+, `(- ∞, 2]`

Miscellaneous Exercise 6 [Pages 130 - 132]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 6 Functions Miscellaneous Exercise 6 [Pages 130 - 132]

Miscellaneous Exercise 6 | Q II. (1) (i) | Page 130

Answer the following:

Identify the following relation is the function? If it is a function determine its domain and range.

{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}

Miscellaneous Exercise 6 | Q II. (1) (ii) | Page 130

Answer the following:

Identify the following relation is the function? If it is a function determine its domain and range.

{(0, 0), (1, 1), (1, –1), (4, 2), (4, –2), (9, 3), (9, –3), (16, 4), (16, –4)}

Miscellaneous Exercise 6 | Q II. (1) (iii) | Page 130

Answer the following:

Identify the following relation is the function? If it is a function determine its domain and range

{(12, 1), (3, 1), (5, 2)}

Miscellaneous Exercise 6 | Q II. (2) (i) | Page 130

Answer the following:

Find whether the following function is one-one

f : R → R defined by f(x) = x2 + 5

Miscellaneous Exercise 6 | Q II. (2) (ii) | Page 130

Answer the following:

Find whether the following function is one-one

f : R − {3} → R defined by f(x) = `(5x + 7)/(x - 3)` for x ∈ R − {3}

Miscellaneous Exercise 6 | Q II. (3) (i) | Page 130

Answer the following:

Find whether the following function is onto or not.

f : Z → Z defined by f(x) = 6x – 7 for all x ∈ Z

Miscellaneous Exercise 6 | Q II. (3) (ii) | Page 130

Answer the following:

Find whether the following function is onto or not.

f : R → R defined by f(x) = x2 + 3 for all x ∈ R

Miscellaneous Exercise 6 | Q II. (4) | Page 130

Answer the following:

Let f: R → R be a function defined by f(x) = 5x3 – 8 for all x ∈ R, show that f is one-one and onto. Hence find f –1 

Miscellaneous Exercise 6 | Q II. (5) | Page 130

Answer the following:

A function f : R → R defined by f(x) = `(3x)/5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f–1

Miscellaneous Exercise 6 | Q II. (6) | Page 130

Answer the following:

A function f is defined as f(x) = 4x + 5, for – 4 ≤ x < 0. Find the values of f(–1), f(–2), f(0), if they exist

Miscellaneous Exercise 6 | Q II. (7) (i) | Page 130

A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 3

Miscellaneous Exercise 6 | Q II. (7) (ii) | Page 130

Answer the following:

A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 5

Miscellaneous Exercise 6 | Q II. (8) | Page 130

Answer the following:

If f(x) = 3x4 – 5x2 + 7 find f(x – 1)

Miscellaneous Exercise 6 | Q II. (9) | Page 130

Answer the following:

If f(x) = 3x + a and f(1) = 7 find a and f(4)

Miscellaneous Exercise 6 | Q II. (10) | Page 130

Answer the following:

If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b

Miscellaneous Exercise 6 | Q II. (11) (i) | Page 130

Answer the following:

Find composite of f and g:
f = {(1, 3), (2, 4), (3, 5), (4, 6)}
g = {(3, 6), (4, 8), (5, 10), (6, 12)}

Miscellaneous Exercise 6 | Q II. (11) (ii) | Page 130

Answer the following:

Find composite of f and g:
f = {(1, 1), (2, 4), (3, 4), (4, 3)}
g = {(1, 1), (3, 27), (4, 64)}

Miscellaneous Exercise 6 | Q II. (12) (i) | Page 130

Answer the following:

Find f ° g and g ° f : f(x) = x2 + 5, g(x) = x – 8

Miscellaneous Exercise 6 | Q II. (12) (ii) | Page 130

Answer the following:

Find f ° g and g ° f: f(x) = 3x – 2, g(x) = x2

Miscellaneous Exercise 6 | Q II. (12) (iii) | Page 130

Answer the following:

Find f ° g and g ° f: f(x) = 256x4, g(x) = `sqrt(x)`

Miscellaneous Exercise 6 | Q II. (13) | Page 130

Answer the following:

If f(x) = `(2x - 1)/(5x - 2), x ≠ 5/2` show that (f ° f) (x) = x

Miscellaneous Exercise 6 | Q II. (14) | Page 131

Answer the following:

If f(x) = `(x + 3)/(4x - 5)`, g(x) = `(3 + 5x)/(4x - 1)` then show that (f ° g) (x) = x

Miscellaneous Exercise 6 | Q II. (15) | Page 131

Answer the following:

Let f : R – {2} → R be defined by f(x) = `(x^2 - 4)/(x - 2)` and g : R → R be defined by g(x) = x + 2. Examine whether f = g or not

Miscellaneous Exercise 6 | Q II. (16) | Page 131

Answer the following:

Let f : R → R be given by f(x) = x + 5 for all x ∈ R. Draw its graph

Miscellaneous Exercise 6 | Q II. (17) | Page 131

Answer the following:

Let f : R → R be given by f(x) = x3 + 1 for all x ∈ R. Draw its graph

Miscellaneous Exercise 6 | Q II. (18) | Page 131

Answer the following:

For any base show that log (1 + 2 + 3) = log 1 + log 2 + log 3

Miscellaneous Exercise 6 | Q II. (19) | Page 131

Answer the following:

Find x, if x = 33log32  

Miscellaneous Exercise 6 | Q II. (20) | Page 131

Answer the following:

Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0

Miscellaneous Exercise 6 | Q II. (21) | Page 131

Answer the following:

Show that, `log ("a"^2/"bc") + log ("b"^2/"ca") + log ("c"^2/"ab")` = 0

Miscellaneous Exercise 6 | Q II. (22) | Page 131

Answer the following:

Simplify, log (log x4) – log (log x)

Miscellaneous Exercise 6 | Q II. (23) | Page 131

Answer the following:

Simplify `log_10  28/45 - log_10  35/324 + log_10  325/432 - log_10  13/15`

Miscellaneous Exercise 6 | Q II. (24) | Page 131

Answer the following:

If `log (("a" + "b")/2) = 1/2(log"a" + log"b")`, then show that a = b

Miscellaneous Exercise 6 | Q II. (25) | Page 131

Answer the following:

If b2 = ac. prove that, log a + log c = 2 log b

Miscellaneous Exercise 6 | Q II. (26) | Page 131

Answer the following:

Solve for x, logx (8x – 3) – logx 4 = 2

Miscellaneous Exercise 6 | Q II. (27) | Page 131

Answer the following:

If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`

Miscellaneous Exercise 6 | Q II. (28) | Page 131

Answer the following:

If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x2 + y2 = 27xy

Miscellaneous Exercise 6 | Q II. (29) | Page 131
Answer the following:
If log3 [log2 (log3x)] = 1, show that x = 6561
Miscellaneous Exercise 6 | Q II. (30) | Page 131

Answer the following:

If f(x) = log(1 – x), 0 ≤ x < 1 show that `"f"(1/(1 + x))` = f(1 – x) – f(– x)

Miscellaneous Exercise 6 | Q II. (31) | Page 131

Answer the following:

Without using log tables, prove that `2/5 < log_10 3 < 1/2`

Miscellaneous Exercise 6 | Q II. (32) | Page 131

Answer the following:

Show that `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)` = log 3

Miscellaneous Exercise 6 | Q II. (33) | Page 131

Answer the following:

Solve : `sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2

Miscellaneous Exercise 6 | Q II. (34) | Page 131

Answer the following:

Find value of `(3 + log_10 343)/(2 + 1/2 log_10 (49/4) + 1/2 log_10 (1/25)`

Miscellaneous Exercise 6 | Q II. (35) | Page 131

Answer the following:

If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1

Miscellaneous Exercise 6 | Q II. (36) | Page 131

Answer the following:

Show that, logy x3 . logz y4 . logx z5 = 60

Miscellaneous Exercise 6 | Q II. (37) | Page 131

Answer the following:

If `log_2"a"/4 = log_2"b"/6 = log_2"c"/(3"k")` and a3b2c = 1 find the value of k

Miscellaneous Exercise 6 | Q II. (38) | Page 131

Answer the following:

If a2 = b3 = c4 = d5, show that loga bcd = `47/30`

Miscellaneous Exercise 6 | Q II. (39) (a) | Page 131

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

1 < |x − 1| < 4

Miscellaneous Exercise 6 | Q II. (39) (b) | Page 131

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

|x2 − x − 6| = x + 2

Miscellaneous Exercise 6 | Q II. (39) (c) | Page 131

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

|x2 − 9| + |x2 − 4| = 5

Miscellaneous Exercise 6 | Q II. (39) (d) | Page 131

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

−2 < [x] ≤ 7

Miscellaneous Exercise 6 | Q II. (39) (e) | Page 131

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

2[2x − 5] − 1 = 7

Miscellaneous Exercise 6 | Q II. (39) (f) | Page 131

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

[x2] − 5[x] + 6 = 0

Miscellaneous Exercise 6 | Q II. (39) (g) | Page 131

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

[x − 2] + [x + 2] + {x} = 0

Miscellaneous Exercise 6 | Q II. (39) (h) | Page 131

Answer the following:

Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function

`[x/2] + [x/3] = (5x)/6`

Miscellaneous Exercise 6 | Q II. (40) (a) | Page 132

Answer the following:

Find the domain of the following function.

f(x) = `(x^2 + 4x + 4)/(x^2 + x - 6)`

Miscellaneous Exercise 6 | Q II. (40) (b) | Page 132

Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - 3) + 1/(log(5 - x))`

Miscellaneous Exercise 6 | Q II. (40) (c) | Page 132

Answer the following:

Find the domain of the following function.

f(x) = `sqrt(1 - sqrt(1 - sqrt(1 - x^2)`

Miscellaneous Exercise 6 | Q II. (40) (d) | Page 132

Answer the following:

Find the domain of the following function.

f(x) = x!

Miscellaneous Exercise 6 | Q II. (40) (e) | Page 132

Answer the following:

Find the domain of the following function.

f(x) = 5–xPx–1

Miscellaneous Exercise 6 | Q II. (40) (f) | Page 132

Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - x^2) + sqrt(5 - x)`

Miscellaneous Exercise 6 | Q II. (40) (g) | Page 132

Answer the following:

Find the domain of the following function.

f(x) = `sqrtlog(x^2 - 6x + 6)`

Miscellaneous Exercise 6 | Q II. (41) (a) | Page 132

Answer the following:

Find the range of the following function.

f(x) = |x – 5|

Miscellaneous Exercise 6 | Q II. (41) (b) | Page 132

Answer the following:

Find the range of the following function.

f(x) = `x/(9 + x^2)`

Miscellaneous Exercise 6 | Q II. (41) (c) | Page 132

Answer the following:

Find the range of the following function.

f(x) = `1/(1 + sqrt(x))`

Miscellaneous Exercise 6 | Q II. (41) (d) | Page 132

Answer the following:

Find the range of the following function.

f(x) = [x] – x

Miscellaneous Exercise 6 | Q II. (41) (e) | Page 132

Answer the following:

Find the range of the following function.

f(x) = 1 + 2x + 4x 

Miscellaneous Exercise 6 | Q II. (42) (a) | Page 132

Answer the following:

Find (f ° g) (x) and (g ° f) (x)

f(x) = ex, g(x) = log x

Miscellaneous Exercise 6 | Q II. (42) (b) | Page 132

Answer the following:

Find (f ° g) (x) and (g ° f) (x)

f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`

Miscellaneous Exercise 6 | Q II. (43) (a) | Page 132

Answer the following:

Find f(x) if g(x) = x2 + x – 2 and (g ° f) (x) = 4x2 – 10x + 4

Miscellaneous Exercise 6 | Q II. (43) (b) | Page 132

Answer the following:

Find f(x) if g(x) = `1 + sqrt(x)` and f[g(x)] = `3 + 2sqrt(x) + x`

Miscellaneous Exercise 6 | Q II. (44) (a) | Page 132

Answer the following:

Find (f ° f) (x) if f(x) = `x/sqrt(1 + x^2)`

Miscellaneous Exercise 6 | Q II. (44) (b) | Page 132

Answer the following:

Find (f ° f) (x) if f(x) = `(2x + 1)/(3x - 2)`

Chapter 6: Functions

Exercise 6.1Exercise 6.2Miscellaneous Exercise 6
Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board - Shaalaa.com

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board chapter 6 - Functions

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board chapter 6 (Functions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board chapter 6 Functions are Concept of Functions, Algebra of Functions.

Using Balbharati 11th solutions Functions exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 11th prefer Balbharati Textbook Solutions to score more in exam.

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