solution is attached.
It is correct that the inverse function is given by the rule . However, it is incorrect to say that the maximal domain of is the same as the domain of the inverse function. The domain of the inverse function is in fact a subset of the maximal domain.
@OP: To find the domain of the inverse function you should recall that . So your job boils down to finding the range of the given function (so it looks like something is left for you to do after all). This job is quite straightforward since you know that f is a one-to-one function ....