Precalculus (6th Edition) Blitzer

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

Chapter 2 - Section 2.2 - Quadratic Functions - Exercise Set - Page 334: 111


The function \[f\left( x \right)={{x}^{4}}-2{{x}^{2}}+1.\]is an even function

Work Step by Step

A function is even when $f\left( x \right)=f\left( -x \right)$ and if $f\left( -x \right)=-f\left( x \right)$, then the function is called an odd function. So, in the above function, replace $x$ with $-x$ and one will obtain: $\begin{align} & f\left( -x \right)={{\left( -x \right)}^{4}}-2{{\left( -x \right)}^{2}}+1 \\ & ={{x}^{4}}-2{{x}^{2}}+1 \\ & =f\left( x \right) \end{align}$ Hence, the above function is an even function.
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