# Misc 1 - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 17, 2018 by Teachoo

Last updated at Dec. 17, 2018 by Teachoo

Transcript

Misc 1 Let f : R R be defined as f(x) = 10x+ 7. Find the function g : R R such that gof= fog= IR Here g is the inverse of f Finding inverse Step 1 f(x) = 10x + 7 Let f(x) = y y = 10x + 7 y 7 = 10x 10x = y 7 x = 7 10 Let g(y) = 7 10 where g: Y N Step 2: gof = g(f(x)) = g(10x + 7) = 10 + 7 7 10 = 10 + 7 7 10 = 10 10 = x = IR Step 3: fog = f(g(y)) = f((๐ฆ โ 7)/10) = 10 ((๐ฆ โ 7)/10) + 7 = y โ 7 + 7 = y + 0 = y = IR Since gof = fog = IR, f is invertible & Inverse of f = g(y) = (๐ โ ๐)/๐๐

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

Ex 1.3, 11

Example 27 Important

Misc 1 You are here

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.