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Finding Inverse

Inverse of function: Proof questions →
Chapter 1 Class 12 Relation and Functions
Concept wise

How to find Inverse?

Last updated at March 16, 2023 by

We find inverse in two scenarios

  1. When f is given as set
  2. When f is given as a function

 

When f is given as set

f = {(1, 4), (2, 5), (3, 6)}

 

In f -1 ,

We reverse all the elements

(1, 4) becomes (4, 1)

(2, 5) becomes (5, 2)

(3, 6) becomes (6, 3)

 

∴ f -1 = {(4, 1), (5, 2), (6, 3)}

 

When f is given as

 f(x) = 2x + 1

 

We put f(x) = y

and find y in terms of x

 

f(x) = 2x + 1

y = 2x + 1

y – 1 = 2x

2x = y – 1

x = (y - 1)/2

 

∴ f -1  = (y - 1)/2

To summarise finding inverse.jpg

 

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.