How to prove:
$f(-x)f(x)$ is an even function.
2026-02-23 11:46:41.1771847201
polynomial even function $f(-x)f(x)$
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Well, a function $g(x)$ is symmetric if $g(-x)=g(x)$.
In your case $g(x) = f(-x)f(x)$ and so $g(-x) = f(-(-x))f(-x) = f(x)f(-x) = f(-x)f(x)=g(x)$.