Let $e(x)$ be an even function and let $o(x)$ be an odd function, such that $e(x) + x^2 = o(x)$ for all $x.$ Let $f(x) = e(x) + o(x).$ Find $f(2).$
We could write $f(x)=e(x)+e(x)+x^2.$
We want to find $f(2),$ so could we write it as $f(2)=e(2)+e(2)+2^2.$ (I'm not sure if we can.)
How would I finish the problem?
If $e(x)$ is an even function, then so is $e(x)+x^2$,
so $e(x)+x^2=o(x)$ means $o(x)$ is an even function and an odd function,
which means that $o(x)=0$, so $e(x)=-x^2$.
Therefore, $f(2)=e(2)+o(2)=-2^2$.