NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2

NCERT Solutions for Class 11 Maths Chapter 2 Exercise 2.2 help students deepen their understanding of relations and functions by exploring more advanced topics related to domain, range, and types of functions. This exercise also covers function notation and understanding how to represent and evaluate functions effectively.

Designed according to the latest CBSE Class 11 Maths syllabus, Exercise 2.2 focuses on different types of functions like one-to-one (injective), onto (surjective), and bijective functions, and how to determine the domain and range of functions. Students will learn to apply these concepts to solve function-related problems systematically.

NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2

Relations and Functions
Easy
Q.
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B).
Relations and Functions
Easy
Q.
If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.
Relations and Functions
Medium
Q.
If A = {–1, 1}, find A × A × A.
Relations and Functions
Easy
Q.
Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.
Relations and Functions
Medium
Q.
Let A = {1, 2, 3,..., 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.
Relations and Functions
Easy
Q.
Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.
Relations and Functions
Medium
Q.
The Fig 2.7 shows a relationship between the sets P and Q. Write this relation.
(i) in set-builder form (ii) roster form.
What is its domain and range?

Relations and Functions
Easy
Q.
Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.
Relations and Functions
Easy
Q.
Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R
Relations and Functions
Medium
Q.
Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.

(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
(ii) {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}
(iii) {(1, 3), (1, 5), (2, 5)}.
Relations and Functions
Medium
Q.
 Find the domain and range of the following real functions:(i)f(x) = – ∣x∣(ii)f(x) = 9−x2 \begin{array}{l}{Find the domain and range of the following real functions:}\\ \begin{array}{l}\left({i}\right){\hspace{0.33em}f}\left({x}\right){ = – }\left|{x}\right|\\ \left({ii}\right){\hspace{0.33em}f}\left({x}\right){ = }\sqrt{{9}-{{x}}^{{2}}}\end{array}\end{array} 
Relations and Functions
Easy
Q.
 If f(x) = x2, find f(1.1) − f(1)(1.1 − 1). \mathrm{If}{ }\mathrm{f}\left(\mathrm{x}\right){ }={ }{\mathrm{x}}^{2},{ }\mathrm{find}{ }\frac{\mathrm{f}\left(1.1\right){ }-{ }\mathrm{f}\left(1\right)}{\left(1.1{ }-{ }1\right)}. 
Relations and Functions
Medium
Q.
 Let R be a relation from N to N defined by R = (a, b): a, b∈N and a = b2. Are the following true?(i) (a,a)∈R, for all a∈N (ii) (a,b)∈R, implies (b,a)∈R(iii) (a,b)∈R, (b,c)∈R implies (a,c)∈R. \begin{array}{l}{Let R be a relation from N to N defined by }\\ {R = {(a, b): a, b}\in {{N and a = b}}^{{2}}{}. }\\ {Are the following true?}\\ {(i) (a,a)}\in {R, for all a}\in {N }\\ {(ii) (a,b)}\in {R, implies (b,a)}\in {R}\\ {(iii) (a,b)}\in {R, (b,c)}\in {R implies (a,c)}\in {R.}\end{array} 

NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2

The solutions are explained in a clear, step-by-step manner so students can confidently identify and work with functions, a key area in higher mathematics.

Question 1: Let A = {1, 2, 3...14}. Define a relation R from A to A by R = {(x,y) : 3x - y = 0}, where x, y are in A. Write down its domain, codomain and range.

  • Answer:
    • Relation R: {(1, 3), (2, 6), (3, 9), (4, 12)}
    • Domain: {1, 2, 3, 4}
    • Codomain: {1, 2, 3...14}
    • Range: {3, 6, 9, 12}

Question 2: Define a relation R on the set N of natural numbers by R = {(x,y) : y = x + 5, x is a natural number less than 4; x, y are in N}. Write the roster form, domain and range.

  • Answer:
    • Roster Form: R = {(1, 6), (2, 7), (3, 8)}
    • Domain: {1, 2, 3}
    • Range: {6, 7, 8}

Question 3: A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y) : the difference between x and y is odd; x is in A, y is in B}. Write R in roster form.

  • Answer: R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}

Question 4: Based on the diagram (P = {5, 6, 7}, Q = {3, 4, 5}), write the relation in (i) set-builder form and (ii) roster form. What is its domain and range?

  • Answer:
    • (i) Set-builder form: R = {(x, y) : y = x - 2; x is in P}
    • (ii) Roster form: R = {(5, 3), (6, 4), (7, 5)}
    • Domain: {5, 6, 7}
    • Range: {3, 4, 5}

Question 5: Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b) : a, b are in A, b is exactly divisible by a}.

  • Answer:
    • (i) Roster form: R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)}
    • (ii) Domain: {1, 2, 3, 4, 6}
    • (iii) Range: {1, 2, 3, 4, 6}

Question 6: Determine the domain and range of the relation R defined by R = {(x, x + 5) : x is in {0, 1, 2, 3, 4, 5}}.

  • Answer:
    • Relation R: {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}
    • Domain: {0, 1, 2, 3, 4, 5}
    • Range: {5, 6, 7, 8, 9, 10}

Question 7: Write the relation R = {(x, x cubed) : x is a prime number less than 10} in roster form.

  • Answer: R = {(2, 8), (3, 27), (5, 125), (7, 343)}

Question 8: Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

  • Answer:
    • n(A x B): 6
    • Number of relations: 2 to the power of 6 (which is 64)

Question 9: Let R be the relation on Z defined by R = {(a, b) : a, b are in Z, a - b is an integer}. Find the domain and range of R.

  • Answer:
    • Domain: Z (all integers)
    • Range: Z (all integers)
    • Reason: The difference between any two integers is always an integer.

FAQs – Class 11 Maths Chapter 2 Exercise 2.2 Relations and Functions

Q1. What is the focus of Exercise 2.2?
Exercise 2.2 focuses on understanding domain and range of functions, exploring types of functions like one-to-one (injective), onto (surjective), and bijective functions.

Q2. How do we determine the domain and range of a function?

  • Domain: The set of all possible input values (x-values) for which the function is defined.

  • Range: The set of all possible output values (y-values) the function can produce from the given domain.

Q3. What is the difference between injective, surjective, and bijective functions?

  • Injective function (One-to-One): Every element of the domain is mapped to a unique element in the range.

  • Surjective function (Onto): Every element of the range is mapped by some element of the domain.

  • Bijective function: A function that is both injective and surjective, meaning each element of the domain is mapped to a unique element of the range, and every element of the range has a corresponding element in the domain.

Q4. Why is Exercise 2.2 important for board exams?
This exercise is crucial as it covers functions, which is a significant topic for Class 11 and 12 exams. Understanding different types of functions and their properties is foundational for calculus and other advanced topics.

Q5. How can students prepare effectively for Exercise 2.2?
Students should focus on:

  • Understanding the concepts of domain and range thoroughly.

  • Practice identifying injective, surjective, and bijective functions.

  • Solve different types of problems involving functions and their notation.