NCERT Solutions for CBSE Class 12 Mathematics ‒ Chapter 1: Relations and Functions (Part III)

Jun 15, 2017 12:30 IST

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2

NCERT Solutions for CBSE Class 12 Maths, Chapter 1: Relations and Functions are available in this article. Here you will get solutions to all the questions of exercise 1.2. Most of the questions given in this exercise are related to the topics relations, functions and their types. These questions are important CBSE Class 12 Maths board exam.

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions (Exercise 1.2) are given below

Question 1: Show that the function f : RR defined by f (x) =1/x is one-one and onto, where R is the set of all non-zero real numbers. Is the result true, if the domain R is replaced by N with co-domain being same as R?

Solution 1:

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 1

NCERT Exemplar Class 12 Mathematics – Chapter 1 Relations and Functions

Question 2: Check the injectivity and surjectivity of the following functions:

(i) f : NN given by f (x) = x2

(ii) f : Z Z given by f (x) = x2

(iii) f : R R given by f (x) = x2

(iv) f : NN given by f (x) = x3

(v) f : ZZ given by f (x) = x3

Solution 2:

(i)

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 2 (i)

(ii)

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 2 (ii)

(iii)

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 2 (iii)

(iv)

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 2 (iv)

(v)

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 2 (v)

NCERT Exemplar Questions & Solutions: CBSE Class 12 Physics – All Chapters

Question 3: Prove that the Greatest Integer Function f : R R, given by f (x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Solution 3:

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 3

Question 4: Show that the Modulus Function f : R R, given by f (x) = | x |, is neither one-one nor onto, where | x | is x, if x is positive or 0 and | x | is – x, if x is negative.

Solution 4:

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 4

Question 5: Show that the Signum Function f : RR, given by

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Q No. 5

Solution 5:

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 5

Question 6: Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one.

Solution 6:

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 6

Question 7: In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

(i) f : RR defined by f (x) = 3 – 4x

(ii) f : R R defined by f (x) = 1 + x2

Solution 7:

(i)

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 7 (i)

(ii)

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 7 (ii)

Question 8: Let A and B be sets. Show that f : A × B → B × A such that f (a, b) = (b, a) is bijective function.

Solution 8:

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 8

Question 9: Let f : NN be defined by

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Q. No. 9

State whether the function f is bijective. Justify your answer.

Solution 9:

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 9

Question 10: Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by f (x) = (x ‒ 2)/(x ‒ 3). Is f one-one and onto? Justify your answer.

Solution 10:

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 10

Question 11: Let f : RR be defined as f(x) = x4. Choose the correct answer.

(A) f is one-one onto

(B) f is many-one onto

(C) f is one-one but not onto

(D) f is neither one-one nor onto.

Solution 11:

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 11

Question 12: Let f : RR be defined as f (x) = 3x. Choose the correct answer.

(A) f is one-one onto

(B) f is many-one onto

(C) f is one-one but not onto

(D) f is neither one-one nor onto.

Solution 12:

NCERT Solutions for CBSE Class 12th Maths, Chapter 1: Relations and Functions, Exercise 1.2, Solution No. 12

Download NCERT Solutions for Class 12 Maths: Chapter 1 Relations and Functions in PDF format

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