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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!

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# Finding Inverse Functions

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