Consider f: given by Show that is invertible with

Given given by We have to show that is invertible.

\section{Injectivity of f:}

Let and be two elements of domain ,

Such that

So, is one-one.

Surjectivity of f:

Let is in the co domain

Such that

(By adding 1 on both sides

in domain

is onto.

So, is a bijection and hence, it is invertible.

Now we have to find

Let

(adding 1 on both sides)

Now substituting this value in (1) we get,

So,