## Precalculus (6th Edition) Blitzer

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