Precalculus (6th Edition) Blitzer

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

Chapter 1 - Test - Page 306: 23

Answer

The value of $f\left( -x \right)$ is $\underline{{{x}^{2}}+x-4}$ and the function is neither odd nor even.

Work Step by Step

We know that the function is said to be even when it satisfies $f\left( x \right)=f\left( -x \right)$ and the function is said to be odd when it satisfies $f\left( x \right)=-f\left( -x \right)$. If the function satisfies neither of the two conditions, then the function is neither even nor odd. To calculate $f\left( -x \right)$ substitute x with $-x$ in the function as follows: $\begin{align} & f\left( -x \right)={{\left( -x \right)}^{2}}-\left( -x \right)-4 \\ & ={{x}^{2}}+x-4 \end{align}$ It is clear that neither $f\left( -x \right)\ne f\left( x \right)$ nor $f\left( -x \right)=-f\left( x \right)$. Therefore, $f$ is neither an even nor an odd function.
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