$f$ is an even function.
Work Step by Step
$f(x) = 1+3x^2 -x^4$ lets calculate $f(-x)$ $f(-x)=1+3(-x)^2 -(-x)^4=1+3(-1)^2x^2 -(-1)^4x^4=1+3x^2 -x^4=f(x)$ Therefore $f$ is an even function.
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