# Math Analysis – Inverse Linear Function

By | November 3, 2016

# Inverse Linear Function

In this tutorial students will learn how to derive the inverse of a linear one-to-one function and then verify those results with the TI-84 Plus C.

First, linear functions are straight lines.

Second, an inverse function can only be created if the original function is one-to-one.  One-to-one means that each x value of the function has only 1 unique y value.  The vertical line test is a visual method to check to see if a function is one-to-one.

Third, for each point on the inverse function there exists a reversed order pair on original function.  Stated another way, the domain and range values are reversed for all points on the graph for both functions.

As an example the point (3,7) has an inverse at point (7,3).

Note that the x values are also called domain or input values.

Note that the y values are also called range or output values.

# Linear Function

$y=2x+6$

# Inverse Function

$y=\frac {1}{2}x-3$

# Graphing Tool

Click the link below to see this problem using an interactive online graphing calculator