Introduction

An*If a function answers the question:*"Alice worked this long; how much money has she made?"*Then its inverse answers the question:*"Alice made this much money; how long did she work?"*If a function answers the question:*"How many hours of music fit on 12 CDs?"*Then its inverse answers the question:*"How many CDs do you need for 3 hours of music?"

If a function is modeled by the rule, , then the inverse function is modeled by . Since multiplication and division are inverse operations, they will create inverse functions.

The function,* f ^{-1}(x)*, is defined as the inverse function of

The inverse has all the same points as the original function, except that the *x* and *y*-coordinates have been reversed. If the point (3,2) is a point in the original function then the point (2,3) will be a point of the inverse function.

It is possible to find the inverse of a set of points, a table, a graph or an equation. The set of points and the table work the same way. All three methods for finding inverses of functions will be discussed here.