NCERT Maths Class 12 Chapter 1 Relations and Functions Notes

Relations and Functions is the first chapter of Class 12 Mathematics and forms the foundation for many advanced mathematical concepts. This chapter helps students understand the relationship between different sets and the rules that connect elements of one set to another.

What are Relations?

A relation is a connection between elements of two sets. It is represented as a set of ordered pairs where the first element belongs to one set and the second element belongs to another set.

Types of Relations

Empty Relation
Universal Relation
Reflexive Relation
Symmetric Relation
Transitive Relation
Equivalence Relation

Understanding these relations helps in analyzing mathematical structures and logical reasoning.

Functions

A function is a special type of relation in which every element of the first set is associated with exactly one element of the second set. Functions are widely used in mathematics, science, economics, and engineering.

Types of Functions

One-One Function

Each element of the domain is mapped to a unique element of the codomain.

Many-One Function

Two or more elements of the domain may have the same image in the codomain.

Onto Function

Every element of the codomain has at least one pre-image in the domain.

Into Function

Some elements of the codomain do not have any pre-image.

Bijective Function

A function that is both one-one and onto.

1 / 0 100%

Composition of Functions

The composition of functions is obtained by applying one function after another. It helps simplify complex mathematical operations and is useful in higher mathematics.

Inverse Functions

An inverse function reverses the action of the original function. Only bijective functions possess inverse functions. Inverse functions are important in algebra, calculus, and mathematical modeling.

Importance of the Chapter

Relations and Functions provide the basis for advanced topics such as calculus, matrices, probability, and differential equations. A clear understanding of this chapter is essential for success in Class 12 Mathematics and competitive examinations.

CBSE Exam Preparation Tips

Students should focus on the concepts of relations, types of functions, composition of functions, and inverse functions. Regular practice of NCERT examples, exercises, and previous years' questions will help strengthen concepts and improve exam performance.

Download

MTG NTA NEET Home Test Series For 2026 Exam