Sec. 7, 9.6-9.7 Due March 2

The sections remind me of some of my high school math classes.  Inverse functions and permutations.  In the section on inverse functions the example of ln(x) and e^x were given.  It states that they are the inverses of one another, but doesn't say how you would go about proving that.  The only method it gave for finding an inverse was swapping x and y in the function and then solving for y.  As the book states that doesn't work in all cases.  What else can be done to prove that functions are inverses of one another?