# Misc 11 - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 24, 2019 by Teachoo

Last updated at Dec. 24, 2019 by Teachoo

Transcript

Misc 11 Let S = {a, b, c} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists. (i) F = {(a, 3), (b, 2), (c, 1)} A function has inverse if it is one-one and onto Check one one F = {(a, 3), (b, 2), (c, 1)} Since each element has unique image, F is one-one Check onto Since for every image, there is a corresponding element, ∴ F is onto. Since function is both one-one and onto it will have inverse F = {(a, 3), (b, 2), (c, 1)} F−1 = {(3, a), (2, b), (1, c)}. Misc 11 Let S = {a, b, c} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists. (ii) F = {(a, 2), (b, 1), (c, 1)} A function has inverse if it is one-one and onto Check one one F = {(a, 2), (b, 1), (c, 1)} Since b & c have the same image 1 F is not one-one Since, F is not one-one, it does not have an inverse

Finding Inverse

Identity Function

Inverse of a function

How to check if function has inverse?

Example 22

Ex 1.3, 5 Important

How to find Inverse?

Example 28

Misc 11 Important You are here

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.