a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2x³ or f(x) = ^{(x + 1)}⁄_{(x – 1)} for x ≠ 1.

Students should know how to find the inverse function of f(x), written f^-1(x). We could just write them backwards (you know, like how supercalifragilisticexpialidocious makes dociousaliexpilisticfragicalirepus), but that would be going a bit too far, don't you think?

If f(x) = y is a function, the inverse function can be found by switching the place of x and y (f(y) = x), and then solving for y so that f^-1(x) = y. For instance, if the function f(x) is y = 2x³, then the inverse function f^-1(x) consists of switching the places of x and y (x = 2y³) and then solving for y.

So if we have function f(x) = 2x³, then its inverse function is:

For functions like , we can't have x = 1 because the denominator cannot equal zero. If we take that precaution, we can solve it for the inverse.

Of course, that means x ≠ 1 for f^-1(x) also. Yes, it's possible for functions to be their own inverses. As long as students can find the inverse of a function given its expression, they're on the right track.