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 .