Suppose we have a function

f(x) = 2x


So, if we input 2, we get 4 back

Inverse 1.jpg


In Inverse of f ,

the opposite happens

i.e. we input 4 and we get 2

Inverse 2.jpg


How to find the inverse?

f(x) = 2x


We put f(x) = y and find x in terms of y

y = 2x

y/2 = x

x = y/2

∴ f -1 (y) = y/2



f(f -1 (x)) will always give back x

i.e. f(f -1 (x)) is an identity function


Let’s check

f -1 (y) = y/2

So, f -1 (x) = x/2


f(f -1 (x)) = f(x/2)

  = 2 (x/2)

  = x




f -1 (f(x)) will always give back x

i.e. f -1 (f(x)) is an identity function


Let’s check

f -1 (f(x)) = f -1 (2x)

  = 2x/2

  = x



f(f -1 (x)) and f -1 (f(x)) are identity functions .


Also, function will have inverse only when it is one-one and onto.

 Let's next see how to check if function has inverse.

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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.