Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.1 Composite Functions and Inverse Functions - 12.1 Exercise Set - Page 789: 93

Answer

The pair of provided functions are inverses of each other.

Work Step by Step

$f\left( x \right)=1.4{{x}^{3}}+3.2$ and $g\left( x \right)=\sqrt[3]{\frac{x-3.2}{1.4}}$ Now, apply the formula for the composition of two functions $f\circ g\left( x \right)=f\left( g\left( x \right) \right)$ Substitute $\sqrt[3]{\frac{x-3.2}{1.4}}$ for $g\left( x \right)$ in the above equation $f\circ g\left( x \right)=f\left( \sqrt[3]{\frac{x-3.2}{1.4}} \right)$ Substitute $\sqrt[3]{\frac{x-3.2}{1.4}}$ for $x$ in the provided function $f\left( x \right)$; the above equation becomes $\begin{align} & f\circ g\left( x \right)=1.4\times {{\left( \sqrt[3]{\frac{x-3.2}{1.4}} \right)}^{3}}+3.2 \\ & =1.4\times \left( \frac{x-3.2}{1.4} \right)+3.2 \\ & =x-3.2+3.2 \\ & =x \end{align}$ Since the compositions equal x, the functions are inverses.
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