# Math Analysis – Inverse Cubic Function

By | November 4, 2016

# Inverse Cubic function

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

# Horizontal Line Test

The inverse of a function can only be found when a function is one-to-one.  A function is one-to-one when it passes the horizontal line test.  The horizontal line test states that for every y value there is one unique x value.

1. Change f(x) to y.
2. Swap x for y & y for x.
3. Solve for y.

# Explicit Function

$f(x)=y=(x+4)^3x$

# Inverse Function

$f^{-1}(x)=\sqrt[3]{x}-4$

# Line of Symmetry

$f(x)=y=x$

# Graphing Tool

Click the link below to see the functions above on an interactive graphing calculator.