Question

The inverse of a function occurs when _____.

Answer 1

⇒When the funtion is both one one and onto , then inverse of the function exists.

⇒≡Consider the function

y=x+2

It is one-one, because for every x there is unique y.So, it is one one.In one-one, there may be some elements in x, which do not have preimage.

It is onto also, because for each x, there is unique y.

So, the inverse of function will be

x=y-2

Replacing x by y and y by x , gives inverse of the function.

y=x-2, is the inverse of the function.