We're given and , and want to show that is 1-1, and then that .
What does a function being 1-1 mean? It means that if two images of the function are equal, then the originating domain elements must also be equal. (y = x^2 isn't 1-1, because a^2 = b^2 doesn't force a = b. y = x^3 is 1-1, since a^3 = b^3 does force a = b.)
Set it up, and then there's an obvious way to proceed. Like this:
Suppose , and .
Then... (fill in the reasoning)...
Therefore f is 1-1.
For , again, go to the definiton, which is that .
For all x in the domain, ...(fill in the reasoning)... .