Founder @ "JEEnlight.com" | YouTube @ "Abhishek Mishra [IIT Kgp]" | PhD in Neuroscience, Germany | IIT Kharagpur B.Tech | Mathematics

Abhishek Mishra

This course is in continuation of the Relations and Functions course for class XI. In this course, we will understand the concept of different types of Relations, functions, composition of functions and Invertible functions. It is a very important chapter for building up the fundamental concepts in Mathematics.

CBSE Class 12

English

Relations and Functions: Class 12 NCERT

Relations & Functions

Mathematics

Class 6-12

Become a topper in your school and ace your board exams by learning from best educators in the country

CBSE

CBSE (Central Board of Secondary Education)

Welcome to the course on Relations & Functions. We have a brief look at the Course Overview.

Relations and Functions: Course Overview

We understand the concept of empty and universal relation.

Types of Relations

We understand the concept of Equivalence relations.

Equivalence Relations

We solve some examples using our knowledge of equivalence relations.

Equivalence Relations Examples

We understand the concept of equivat classes, and importance of equivalence relations.

Equivalence Class

We solve one more example for Equivalence relation and briefly review how we define functions.

Functions

We understand the concept of One-One & Onto functions.

Type of Functions : One-One , Onto

We solve some examples based on One-One & Onto functions.

One - One and Onto Functions

We solve some examples to check One-One & onto function

Solved Examples

We solve some more examples of One-One and onto.

Solved Examples - Part II

We understand the concept of composition of functions.

Composition of Functions

We solve some more examples using our knowledge of composition of functions.

Composition of Function - Solved Examples

We understand that if both f and g are onto or if both f and g are one - one, then composite function gof will also be onto or One-One respectively.

Composition of functions - Relation with One-One, Onto

We understand that if composition of function gof is onto, then it implies that g has to be onto. And if gof is One-One, then it implies that f has to be one-one.

Composition of functions : Onto, One-One

We introduce the concept of Invertible functions.

Invertible Function

We formally define Invertible function and go through an example.

Invertible function Definition

We solve some examples based on our concept of Invertible functions.

Invertible function - Solved Examples

Composition of three functions f,g,h

We understand the concept of binary operation.

Binary Operation.

We solve some examples using our knowledge of binary operations.

Binary Operation Examples

We understand the concept of operation tables.

Operation Tables

We understand the Commutative & Associative Property of binary operations.

Commutative, Associative Property

We understand the concept of identity element.

Identity element for a binary operation

We understand the concept of inverse of an element.

Inverse element for a binary operation

Miscellaneous Examples

We solve some more miscellaneous problems.

Miscellaneous Examples : Part II

We have a look at some more miscellaneous examples.

Miscellaneous Examples : Part III

We solve some final miscellaneous examples.

Miscellaneous Examples - Part IV

B.Sc. (hons) Maths || M.Sc Maths || GATE Exam AIR - 94 || Educator || SME - Mathematics

Ekta Jain

This course discusses about the chapter 1 (Relations and  Functions), N.C.E.R.T , class 12 (CBSE).

(Hindi) Relations and Functions - Class 12

R B Gautam

Matrices have been covered in full in this course. It has questions based on matrices.

(Hindi) Matrices

Pursuing PhD in Biomedical Engg from IIT Bombay, M.Tech in VLSI from NIT Kurukshetra, cleared GATE and UGC-NET. Love teaching❤️

Ria Paul

The course lets you know about various types of relations, functions, inverse of functions and binary operations on functions.

Relations and Functions

Bijendra Kumar Guddu

In this course, the educator is discussing Relations and Functions for Class 12th Aspirants

Lessons

28 lessons • 5h 7m

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Relations and Functions: Course Overview

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Types of Relations

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Equivalence Relations

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Equivalence Relations Examples

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Equivalence Class

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Functions

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Type of Functions : One-One , Onto

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One - One and Onto Functions

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Solved Examples

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Solved Examples - Part II

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