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

#### Chapters ## 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

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

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

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

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

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

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

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

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

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

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

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

If f(x) = 3x4 – 5x2 + 7 find f(x – 1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Find x, if x = 33log32

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

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

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

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

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

Simplify, log (log x4) – log (log x)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Find the domain of the following function.

f(x) = x!

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

Find the domain of the following function.

f(x) = 5–xPx–1

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

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

Find the domain of the following function.

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

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

Find the range of the following function.

f(x) = |x – 5|

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

Find the range of the following function.

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

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

Find the range of the following function.

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

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

Find the range of the following function.

f(x) = [x] – x

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

Find the range of the following function.

f(x) = 1 + 2x + 4x

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

Find (f ° g) (x) and (g ° f) (x)

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

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

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

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

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

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

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

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

## Chapter 6: Functions

Exercise 6.1Exercise 6.2Miscellaneous Exercise 6 ## Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board chapter 6 - Functions

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