Precalculus (6th Edition) Blitzer

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

Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set - Page 260: 116

Answer

The statement is false. The correct statement is, “If $f\left( 7 \right)=35$ and $g\left( 4 \right)=7$ , then $\left( f\circ g \right)\left( 4 \right)=35$.” (One possible answer.)

Work Step by Step

Find: $\begin{align} & f\left( g\left( 4 \right) \right)=f\left( 7 \right) \\ & =5 \end{align}$. $f\left( g\left( 4 \right) \right)\ne 35$ Hence, the given statement is false. We can change the statement to: If $f\left( 7 \right)=35,g\left( 4 \right)=7$ , then $\begin{align} & f\left( g\left( 4 \right) \right)=f\left( 7 \right) \\ & =35 \end{align}$
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