Answer
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.
