Subscribe to our Youtube Channel - https://you.tube/teachoo

Last updated at Jan. 28, 2020 by Teachoo

Transcript

Ex 1.3, 5 State with reason whether following functions have inverse (i) f: {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)} A function has inverse if it is one-one and onto Check one one f = {(1, 10), (2, 10), (3, 10), (4, 10)} Since all elements have image 10, They do not have unique image ∴ f is not one-one. Since, f is not one-one, it does not have an inverse. Ex 1.3, 5 State with reason whether following functions have inverse (ii) g: {5, 6, 7, 8} → {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)} A function has inverse if it is one-one and onto Check one one g = {(5, 4), (6, 3), (7, 4), (8, 2)} Since, 5 & 7 have same image 4 g is not one-one Since, g is not one-one, it does not have an inverse Ex 1.3, 5 State with reason whether following functions have inverse (iii) h: {2, 3, 4, 5} → {7, 9, 11, 13} with h = {(2, 7), (3, 9), (4, 11), (5, 13)} A function has inverse if it is one-one and onto Check one one h = {(2, 7), (3, 9), (4, 11), (5, 13)} Since each element has unique image, h is one-one Check onto Since for every image, there is a corresponding element, ∴ h is onto. Since function is both one-one and onto it will have inverse h = {(2, 7), (3, 9), (4, 11), (5, 13)} h-1 = {(7, 2), (9, 3), (11, 4), (13, 5)}

Finding Inverse

Identity Function

Inverse of a function

How to check if function has inverse?

Example 22

Ex 1.3, 5 Important You are here

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.