Answer
The function is even.
Work Step by Step
$f(x)=2x^{2}+x^{4}+1$
Substitute $x$ by $-x$ in $f(x)$ and simplify:
$f(-x)=2(-x)^{2}+(-x)^{4}+1$
$f(-x)=2x^{2}+x^{4}+1$
Since $f(x)=f(-x)$, the function is even
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