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

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* : **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**

**?**

_{∗}**Solution 1:**

**
**

**NCERT Exemplar Class 12 Mathematics – Chapter 1 Relations and Functions**

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

**(i) ***f* : **N** → **N** given by *f *(*x*) = *x*^{2}

**(ii) ***f* : ** Z **→

**given by**

*Z**f*(

*x*) =

*x*

^{2}

**(iii)** *f* : ** R **→

**given by**

*R**f*(

*x*) =

*x*

^{2}

**(iv) ***f *: ** N** →

**given by**

*N**f*(

*x*) =

*x*

^{3}

**(v) ***f *: **Z** → **Z **given by *f* (*x*) = *x*^{3}

**Solution 2:**

**(i)**

**
**

**(ii)**

**
**

**(iii)**

**
**

**(iv)**

**
**

**(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:**

**
**

**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:**

**
**

**Question 5:** Show that the Signum Function *f* : **R** → **R**, given by

**Solution 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:**

**
**

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

(*i*) *f* : **R** → **R** defined by *f* (*x*) = 3 – 4*x*

(*ii*) *f* : **R **→ **R** defined by *f* (*x*) = 1 + *x*^{2}

**Solution 7:**

**(i)**

**
**

**(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:**

**
**

**Question 9:** Let *f *: **N** → **N** be defined by

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

**Solution 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:**

**
**

**Question 11:** Let *f* :** R** → **R** be defined as f(x) =* x ^{4}*. 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:**

**
**

**Question 12:** Let *f *: **R** → **R** be defined as *f *(*x*) = 3*x*. 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:**

**
**

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