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 259: 86


The value of $\left( \frac{g}{f} \right)\left( 3 \right)$ is $0$.

Work Step by Step

Curve ${{C}_{1}}$ represents the values of the function $f\left( x \right)$ and curve ${{C}_{2}}$ represents the values of the function $g\left( x \right)$. To calculate the value of $\left( \frac{g}{f} \right)\left( 3 \right)$: Recall that: $\left( \frac{g}{f} \right)\left( x \right)=\frac{g\left( x \right)}{f\left( x \right)}$ …… (I) Therefore, the value of $f\left( 3 \right)=-3$ and $g\left( 3 \right)=0$ Apply the equation (I), $\begin{align} & \left( \frac{g}{f} \right)\left( 3 \right)=\frac{g\left( 3 \right)}{f\left( 3 \right)} \\ & =\frac{0}{-3} \\ & =0 \end{align}$ Hence, the value of $\left( \frac{g}{f} \right)\left( 3 \right)$ is $0$.
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