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## Chapter 2: Functions

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 2 Functions Exercise 2.1 [Pages 30 - 31]

**Check if the following relation is function:**

**Check if the following relation is function:**

**Check if the following relation is function:**

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)}

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)}

Which set of ordered pair represent function from A = {1, 2, 3, 4}to B = {−1, 0, 1, 2, 3}? Justify : {(1, 3), (4,1), (2, 2)}

Which set of ordered pair represent function from A = {1, 2, 3, 4}to B = {−1, 0, 1, 2, 3}? Justify : {(1, 1), (2, 1), (3, 1), (4, 1)}

If f(m) = m^{2 }− 3m + 1, find f(0)

If f(m) = m^{2} − 3m + 1, find f(−3)

If f(m) = m^{2} − 3m + 1, find `f(1/2)`

If ƒ(m) = m^{2} − 3m + 1, find f(x + 1)

If f(m) = m^{2} − 3m + 1, find f(− x)

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

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

Find x, if `"g"(x)` = 0 where `"g"(x)` = 6x^{2} + x − 2

Find x, if f(x) = g(x) where f(x) = x^{4 }+ 2x^{2} , g(x) = 11x^{2}

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

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

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

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

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

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

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

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

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

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

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

If f(x) = 2x^{2} + 3, g(x) = 5x − 2, then find fog.

If f(x) = 2x^{2} + 3, g(x) = 5x − 2, then find gof.

If f(x) = 2x^{2} + 3, g(x) = 5x – 2, then find fof.

If f(x) = 2x^{2} + 3, g(x) = 5x – 2, then find gog.

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 2 Functions Miscellaneous Exercise 2 [Page 32]

Which of the following relations are functions? If it is a function determine its domain and range:

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

Which of the following relations are functions? 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)}

Which of the following relations are functions? If it is a function determine its domain and range:

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

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}.

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

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

If f(x) = 3x^{2 }− 5x + 7 find f(x − 1).

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

If f(x) = ax^{2} + bx + 2 and f(1) = 3, f(4) = 42, find a and b.

If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x

If f(x) = `(x+3)/(4x−5) , "g"(x) = (3+5x)/(4x−1)` then verify that `("fog") (x)` = x.

## Chapter 2: Functions

## Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 2 - Functions

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Concepts covered in Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 2 Functions are Types of Functions, Representation of Function, Graph of a Function, Fundamental Functions, Algebra of Functions, Composite Function, Inverse Functions, Some Special Functions, Concept of Functions.

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