# 12th CBSE Math Guide - Relations and Functions, NCERT Solutions of Exercise 1.2

### CBSE Guide NCERT Solutions for Class 12 Mathematics

Chapter 1, relations and functions
Cbse Ncert Solution of XII Math Textbook Exercise 1.2
(Solutions of CBSE Class 12  NCERT Maths Exercise 1.2, Relations and Functions)
Scroll down and click on the Link in between & at the end of Questions to open Solutions (pdf)
Question 1: Show that the function f: R* → R* 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*?
Question 2: Check the injectivity and surjectivity of the following functions:
(i) f: N → N 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: N → N given by f(x) = x3
(v) f: Z → Z given by f(x) = x3
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.
Class XII CBSE Maths - NCERT Solutions of Relations and Functions Ex 1.2
Question 4: Show that the Modulus Function f: R → R given by, is neither one-one nor onto, where |x| is x, if x is positive or 0 and |x| is − x, if x is negative.
Question 5: Show that the Signum Function f: R → R, given by
is neither one-one nor onto.
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.
Question 7: In each of the following cases, state whether the function is one-one, onto or bijective.
(i) f: R → R defined by f(x) = 3 − 4x
(ii) f: R → R defined by f(x) = 1 + x2
Question 8: Let A and B be sets. Show that f: A × B B × A such that (a, b) = (b, a) is bijective function.
Relations and Functions - Class 12 Mathematics CBSE Guide NCERT Solutions

Question 9:

Question 10: Let A = R − {3} and B = R − {1}. Consider the function f: A → B defined by