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Last updated at July 5, 2019 by Teachoo

Transcript

Example 22 Let f : {1, 2, 3} {a, b, c} be one-one and onto function given by f (1) = a, f(2) = b and f (3) = c. Show that there exists a function g : {a, b, c} {1, 2, 3} such that gof= IX and fog = IY, where, X = {1, 2, 3} and Y = {a, b, c}. Finding gof So, gof = { (1, 1) , (2, 2), (3, 3) } = IX = Identity function on set X = {1, 2, 3} Finding fog fog = { (a, a) , (b, b), (c, c) } = IY = Identity function on set Y = {a, b, c}

Finding Inverse

Identity Function

Inverse of a function

How to check if function has inverse?

Example 22 You are here

Ex 1.3, 5 Important

How to find Inverse?

Example 28

Misc 11 Important

Ex 1.3, 11

Example 27 Important

Misc 1

Ex 1.3 , 6

Ex 1.3 , 14 Important

Example 23 Important

Misc 2

Ex 1.3 , 4

Example 24

Ex 1.3 , 8 Important

Example 25 Important

Ex 1.3 , 9 Important

Chapter 1 Class 12 Relation and Functions

Concept wise

- Relations - Definition
- Empty and Universal Relation
- To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
- To prove one-one & onto (injective, surjective, bijective)
- Composite functions
- Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.