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

 

Now,

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

 

 

Similarly,

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

 

Thus,

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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo