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Last updated at May 29, 2018 by Teachoo

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Ex1.3 , 4 If 𝑓(𝑥)=(4𝑥 − 3)6𝑥 − 4, 𝑥 ≠ 23 , show that 𝑓𝑜𝑓(𝑥)=𝑥, for all 𝑥 ≠ 23 . What is the inverse of f? 𝑓(𝑥)=(4𝑥 − 3)6𝑥 − 4 𝑓(𝑓𝑥) = 4𝑓(𝑥) − 36𝑓(𝑥) − 4 𝑓𝑜𝑓𝑥 = 44𝑥 − 36𝑥 − 4 − 364𝑥 − 36𝑥 − 4 − 4 = 44𝑥 − 3 − 36𝑥 − 46𝑥 − 464𝑥 − 3 − 46𝑥 − 46𝑥 − 4 = 16𝑥 − 12 − 18𝑥 +126𝑥 − 424𝑥 − 18 − 24𝑥 +166𝑥 − 4 = 16𝑥 − 12 − 18𝑥 +126𝑥 − 4 × 6𝑥 − 424𝑥 − 18 − 24𝑥 + 16 = 16𝑥 − 12 − 18𝑥 +1224𝑥 −18 −24𝑥 +16 = −2𝑥 + 00 − 2 = −2𝑥− 2 = x ∴ 𝑓𝑜𝑓𝑥 = x Calculating inverse of f(x) 𝑓(𝑥)=(4𝑥 − 3)6𝑥 − 4 Put f(x) = y y = (4𝑥 − 3)6𝑥 − 4 y(6x – 4) = (4x – 3) 6xy – 4y = 4x – 3 6xy – 4x = 4y – 3 x(6y – 4) = 4y – 3 x = 4𝑦 − 36𝑦 − 4 So, inverse of f = 4𝑦 − 36𝑦 − 4 ∴ Let inverse of f = g (y) = 4𝑦 − 36𝑦 − 4 g (y) = 4𝑦 − 36𝑦 − 4 Replacing y with x g (x) = 4𝑥 − 36𝑥 − 4 = f(x) Hence we can say inverse of f is f itself i.e. f -1 = f

Finding Inverse

Identity Function

Inverse of a function

How to check if function has inverse? Not in Syllabus - CBSE Exams 2021

Example 22 Not in Syllabus - CBSE Exams 2021

Ex 1.3, 5 Important Not in Syllabus - CBSE Exams 2021

How to find Inverse?

Example 28 Not in Syllabus - CBSE Exams 2021

Misc 11 Important Not in Syllabus - CBSE Exams 2021

Ex 1.3, 11 Not in Syllabus - CBSE Exams 2021

Example 27 Important Not in Syllabus - CBSE Exams 2021

Misc 1 Not in Syllabus - CBSE Exams 2021

Ex 1.3 , 6 Not in Syllabus - CBSE Exams 2021

Ex 1.3 , 14 Important Not in Syllabus - CBSE Exams 2021

Example 23 Important Not in Syllabus - CBSE Exams 2021

Misc 2 Not in Syllabus - CBSE Exams 2021

Ex 1.3 , 4 Not in Syllabus - CBSE Exams 2021 You are here

Example 24 Not in Syllabus - CBSE Exams 2021

Ex 1.3 , 8 Important Not in Syllabus - CBSE Exams 2021

Example 25 Important Not in Syllabus - CBSE Exams 2021

Ex 1.3 , 9 Important Not in Syllabus - CBSE Exams 2021

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.