Step 1:

The function is .

The function is continuous in the interval .

Derivative of is , which i positive in the interval .

So the function is one to one function and is strictly monotonic.

Now We have to find the inverse of the function.

Consider , then .

Substitute in the above expression.

Interchange .

Then .

So the inverse of the function is .

Step 2:

The inverse function is  

Apply derivative on each side with respect to .

.

Now we need to find .

.

Solution :

The function is f is monotonic and has an inverse .

.