Precalculus (6th Edition) Blitzer

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

Chapter 2 - Cumulative Review Exercises - Page 435: 4

Answer

The value of $\left( f\circ f \right)\left( -1 \right)$ is $3$.

Work Step by Step

$\left( f\circ f \right)$ is defined as the composition of f with f. $\left( f\circ f \right)\left( x \right)=f\left( f\left( x \right) \right)$ Here, substitute x with $f\left( x \right)$ in the expression of the function. In order to find the value of $\left( f\circ f \right)\left( -1 \right)=f\left( f\left( -1 \right) \right)$ , first find the value of $f\left( -1 \right)$. It has been observed that $x=-1$ is a zero of the function. Thus, $f\left( -1 \right)=0$. Substitute the value of $f\left( -1 \right)$ in $f\left( f\left( -1 \right) \right)$. $f\left( f\left( -1 \right) \right)=f\left( 0 \right)$ Also, $f\left( 0 \right)=3$. $\begin{align} & \left( f\circ f \right)\left( -1 \right)=f\left( f\left( -1 \right) \right) \\ & =f\left( 0 \right) \\ & =3 \end{align}$ Therefore, the value of $\left( f\circ f \right)\left( -1 \right)$ is $3$.
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