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

## Chapter 2: Functions

Exercise 2.1Miscellaneous Exercise 2
Exercise 2.1 [Pages 30 - 31]

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

Exercise 2.1 | Q 1. (a) | Page 30

Check if the following relation is function:

Exercise 2.1 | Q 1. (b) | Page 31

Check if the following relation is function:

Exercise 2.1 | Q 1. (c) | Page 31

Check if the following relation is function:

Exercise 2.1 | Q 2. (a) | Page 31

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 2.1 | Q 2. (b) | Page 31

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 2.1 | Q 2. (c) | Page 31

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)}

Exercise 2.1 | Q 2. (d) | Page 31

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)}

Exercise 2.1 | Q 3. (a) | Page 31

If f(m) = m2 − 3m + 1, find f(0)

Exercise 2.1 | Q 3. (b) | Page 31

If f(m) = m2 − 3m + 1, find f(−3)

Exercise 2.1 | Q 3. (c) | Page 31

If f(m) = m2 − 3m + 1, find f(1/2)

Exercise 2.1 | Q 3. (d) | Page 31

If ƒ(m) = m2 − 3m + 1, find f(x + 1)

Exercise 2.1 | Q 3. (e) | Page 31

If f(m) = m2 − 3m + 1, find f(− x)

Exercise 2.1 | Q 4. (a) | Page 31

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

Exercise 2.1 | Q 4. (b) | Page 31

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

Exercise 2.1 | Q 4. (c) | Page 31

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

Exercise 2.1 | Q 5 | Page 31

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

Exercise 2.1 | Q 6. (a) | Page 31

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

Exercise 2.1 | Q 6. (b) | Page 31

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

Exercise 2.1 | Q 6. (c) | Page 31

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

Exercise 2.1 | Q 7. (a) | Page 31

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

Exercise 2.1 | Q 7. (b) | Page 31

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

Exercise 2.1 | Q 7. (c) | Page 31

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

Exercise 2.1 | Q 7. (d) | Page 31

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

Exercise 2.1 | Q 8. (a) | Page 31

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

Exercise 2.1 | Q 8. (b) | Page 31

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

Exercise 2.1 | Q 8. (c) | Page 31

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

Exercise 2.1 | Q 8. (d) | Page 31

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

Exercise 2.1 | Q 9. (a) | Page 31

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

Exercise 2.1 | Q 9. (b) | Page 31

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

Exercise 2.1 | Q 9. (c) | Page 31

If f(x) = 2x2 + 3, g(x) = 5x – 2, then find fof.

Exercise 2.1 | Q 9. (d) | Page 31

If f(x) = 2x2 + 3, g(x) = 5x – 2, then find gog.

Miscellaneous Exercise 2 [Page 32]

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

Miscellaneous Exercise 2 | Q 1. (i) | 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)}

Miscellaneous Exercise 2 | Q 1. (ii) | Page 32

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)}

Miscellaneous Exercise 2 | Q 1. (iii) | Page 32

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

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

Miscellaneous Exercise 2 | Q 2 | Page 32

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 2 | Q 3 | Page 32

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.

Miscellaneous Exercise 2 | Q 4 | Page 32

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

Miscellaneous Exercise 2 | Q 5 | Page 32

If f(x) = 3x2 − 5x + 7 find f(x − 1).

Miscellaneous Exercise 2 | Q 6 | Page 32

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

Miscellaneous Exercise 2 | Q 7 | Page 32

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

Miscellaneous Exercise 2 | Q 8 | Page 32

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

Miscellaneous Exercise 2 | Q 9 | Page 32

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

## Chapter 2: Functions

Exercise 2.1Miscellaneous Exercise 2

## 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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