# Inverse Function

- Author:
- Dr. Doug Davis, 3D

## Description

A function converts an value to a value so the inverse operation would take a value back to the original value. Because the inverse operation would take a value to an value the axis and names are switched. The inverse operation of a function can be shown on a graph by reflecting the function about the line which is equivalent to switching the and axes.
The inverse of a function is labeled as . However, not all functions have inverse functions. You can enter a function in the entry box. This applet will then tell whether the inverse operation is a function. This test is performed only on the visible portion of the domain of the inverse operation.
Checking the "Path" checkbox will show the path of numbers. By moving the initial x value ( the orange plus ) it can be seen that if is a function. Also, from exchange of functions

## Activities

Determine what requirement must the original function satisfy in order to have an inverse function.
Also, note the Domain and Range of the function and inverse operation.
Is there a way to limit the domain or range of the flipped function so that it could be a function.