Precalculus (6th Edition) Blitzer

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

Chapter 1 - Section 1.8 - Inverse Functions - Exercise Set - Page 270: 63


\[g\left( f\left[ h\left( 1 \right) \right] \right)=11\]

Work Step by Step

The value of the given composite function can be obtained using the definition of composite functions and the values of $f$ , $g$ and $h$ at the required points. Now, $h\left( 1 \right)={{1}^{2}}+1+2=4$ , thus we have $\begin{align} & g\left( f\left[ h\left( 1 \right) \right] \right)=g\left( f\left[ 4 \right] \right) \\ & =g\left( 2\times 4-5 \right) \\ & =g\left( 3 \right) \end{align}$ Now simplify further to get, $\begin{align} & g\left( 3 \right)=4\left( 3 \right)-1 \\ & =11 \end{align}$
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