The functions  and  are one-to-one functions.

(a)

If a function is an inverse, then it has to be a one-to-one to be a funtion.

.

Since  is a one to one function, then there exist inverse of the function such that .

Then there exists  and .

.

Since  is a one to one function, then there exist inverse of the function such that .

 and .

As  and  are one-to-one functions then .

.

 is one-to-one.

(b)

 and .

let

 and 

Then, 

Therefore,

Therefore the statement is true and .