In this lesson you will learn how to determine the inverse of a function given in a variety of representations such as a table, graph, mapping diagram, equation, or verbal form.

Let's first begin with what is an inverse relation and inverse function.

The inverse of the relation consisting of all ordered pairs (x,y) is the set of all ordered pairs (y,x). The graph of an inverse relation is the reflection of the graph of the relation across the line y = x.

The function that results from exchanging the input and output values of a one-to-one function is called the inverse function. The inverse of f(x) is denoted f -1(x).

This is a mapping diagram of a function and its inverse
Source: Inverse Function, Jim Belk, Wikimedia		 This is a picture of a graph and its inverse.
Source: Inverse Function Graph, Jim Belk, Wikimedia

To better understand finding inverses of functions watch the following Video Clip. Identify the different methods used in the video to determine inverses.

Video segment. Assistance may be required.

Source: Inverse Relations and Functions, gdawgrapper, YouTube