# NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.3

NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.3 Relations and Functions in Hindi Medium as well as English Medium for CBSE Board, MP Board, UP Board, Bihar and Uttarakhand (UK Board), etc, for 2021-22.

NCERT Solutions or UP Board solutions are applicable for all boards who are using NCERT Textbooks 2021-2022 for their exams.## NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.3

### Class 12 Maths Exercise 1.3 Solutions in Hindi & English

Class: 12 | Maths (English and Hindi Medium) |

Chapter 1: | Exercise 1.3 |

### 12th Maths Exercise 1.3 Solutions

NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.3 Relations and Functions in English Medium PDF to download free to use it offline updated for new academic session 2021-22. All NCERT solutions are updated according to NCERT Books 2021-22 on the basis of latest CBSE Syllabus. Ask your doubts related to NIOS board as well as CBSE Board through Discussion Forum. This is a platform for sharing of knowledge with each other.

#### Class 12 Maths Exercise 1.3 Solution in Videos

#### About 12 Maths Exercise 1.3

In Exercise 1.3 of Relations and Functions, the questions are based on one – one and onto relations. If a relation is one – one and onto, then it is called invertible relations and hence the inverse of the relation exists. The knowledge of the concepts of Exercise 1.1, as to fog and gof will be implemented in this exercise. All the questions are done in simplified way, so that students of English Medium as well as Hindi Medium can understand easily. If you still find any difficulty to understand the solutions, please notify us, we will try to simplified further as much as possible. Our only aim to prepare the contents which are on user friendly interface as well as easy to learn.

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##### What are the main concepts on which exercise 1.3 of grade 12th Maths is based?

There are two main concepts on which exercise 1.3 of grade 12th Maths is based. These concepts are:

1. **Compositions of Functions**.

Let f: A → B and g: B → C be two functions. Then the composition of f and g, denoted by gof, is defined as the function gof: A → C given by gof(x) = g(f(x)), ∀ x ∈ A.

2. **Invertible Function**.

If f is invertible, then f must be one-one and onto and conversely, if f is one-one and onto, then f must be invertible. This fact significantly helps for proving a function f to be invertible by showing that f is one-one and onto, specially when the actual inverse of f is not to be determined.

##### How long it take to prepare exercise 1.3 (chapter 1) of class 12th Maths?

Students need a maximum of four days to prepare exercise 1.3 (chapter 1) of class 12th Maths if they give 1-2 hours per day to this exercise. This time also depends on student’s working speed, efficiency, capability, and many other factors.

##### Is exercise 1.3 of Class12th Maths important for 1st Term Exams?

Yes, exercise 1.3 of grade 12th Maths is important from the exam point of view. Every year questions are asked from this exercise in the board exams. All the questions of this exercise are important and can come in the exams. But the most important questions of this exercise are examples 18, 19, 20, 21, 23, 25, 27 and questions 3, 5, 6, 8, 9, 10, 13, 14.

##### In which type of questions of exercise 1.3 (class 12th Maths), students face problems while solving?

In exercise 1.3 of grade 12th Maths, most students face problems in those questions in which they have to find out the inverse of a given function.

##### What are the theorems to know before doing exercise 1.3 of grade 12th Maths?

There are two theorems before exercise 1.3 of grade 12th Maths.

Two theorems are:

1. If f: X → Y, g: Y → Z and h: Z → S are functions, then ho(gof)=(hog)of.

2. Let f: X → Y and g: Y → Z be two invertible functions. Then gof is also invertible with (gof)⁻¹ = f⁻¹o g⁻¹.