Precalculus (6th Edition) Blitzer

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

Chapter 1 - Test - Page 306: 34

Answer

The two functions which compose the function $h\left( x \right)$ are $f\left( x \right)={{x}^{7}}$ and $g\left( x \right)=\left( 2x+3 \right)$.

Work Step by Step

It is known that the composition of the function means applying one function to the output of another function. Composition is denoted by: $\left( f\circ g \right)\left( x \right)=f\left( g\left( x \right) \right)$. Let $g\left( x \right)$ be a function as $g\left( x \right)=\left( 2x+3 \right)$ . Let another function $f\left( x \right)$ be $f\left( x \right)={{x}^{7}}$. Now, $\begin{align} & \left( f\circ g \right)\left( x \right)=f\left( g\left( x \right) \right) \\ & =f\left( 2x+3 \right) \\ & ={{\left( 2x+3 \right)}^{7}} \end{align}$ So, the function $h\left( x \right)$ is the composition of two functions $f\left( x \right)$ and $g\left( x \right)$.
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