Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Review Exercises - Page 303: 105

Answer

The function $h\left( x \right)=\sqrt[3]{7x+4}$ can be written as composition of the functions $f\left( x \right)=\sqrt[3]{x}\text{ and }g\left( x \right)=7x+4$.

Work Step by Step

Consider the functions $f\left( x \right)=\sqrt[3]{x}$ and $g\left( x \right)=7x+4$. Then, $\begin{align} & h\left( x \right)=\sqrt[3]{7x+4} \\ & =f\left( 7x+4 \right) \\ & =f\left( g\left( x \right) \right) \end{align}$ Hence, the function $h\left( x \right)=\sqrt[3]{7x+4}$ can be written as composition of the functions $f\left( x \right)=\sqrt[3]{x}\text{ and }g\left( x \right)=7x+4$.
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