The function is .

The domain of a function is all values of  which makes the function mathematically correct.

.

Since the function has no variable, domain of the function cannot be defined.

The function is .

Apply derivative on each side with respect to .

.

The derivative of the function is zero.

Hence no conclusions can be made.

A one to one function is a function which takes only one value of  for any .

The function is constant function, hence for any value of , the value of function is .

Hence, the function is not one to one function.

Inverse of the function does not exist.

The function is not one to one and the inverse of the function does not exist.