Hi everyone... I am currently teaching summer Precalculus at the University of New Hampshire, and I have come to the section on inverse functions. I have no problems relating the basic definitions: one-to-one, horizontal line test, etc., but I am looking for clarification on one point. When we teach students how to "find" inverse functions, the steps are usually the same: I. Confirm that function y=f(x) is one-to-one. II. Solve for x (if possible). III. Switch the variables so that you have y = f-1(x). So, I have two questions. Please answer them by number. 1. Using precalculus mathematics, can we always perform the second step (solving for x)? I hate to use the words "never" or "impossible" with students unless I really mean it. As an example, is there a way to write the inverse of y = x^3 + x? 2. Using non-precalculus methods, can we... (same question). Thanks!