Answer
This function is even.
Work Step by Step
$f(x)=\dfrac{1}{5}x^{6}-3x^{2}$
Substitute $x$ by $-x$ in $f(x)$ and simplify:
$f(-x)=\dfrac{1}{5}(-x)^{6}-3(-x)^{2}=\dfrac{1}{5}x^{6}-3x^{2}$
Since $f(x)=f(-x)$, this function is even.
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