Check sibling questions

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 of a function - Part 2


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 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.