Precalculus (6th Edition) Blitzer

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

Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 178: 98


The value of $f\left( -x \right)-f\left( x \right)$ is $6x$.

Work Step by Step

By replacing x by –x in the given function, we get the expression for $f\left( -x \right)$ as follows $\begin{align} & f\left( -x \right)={{\left( -x \right)}^{2}}-3\left( -x \right)+7 \\ & ={{x}^{2}}+3x+7 \end{align}$ So, calculate the value of the expression $f\left( -x \right)-f\left( x \right)$ as follows $\begin{align} & f\left( -x \right)-f\left( x \right)={{x}^{2}}+3x+7-\left( {{x}^{2}}-3x+7 \right) \\ & ={{x}^{2}}+3x+7-{{x}^{2}}+3x-7 \\ & =6x \end{align}$ Therefore, the given value of $f\left( -x \right)-f\left( x \right)$ is $6x$.
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