Do there exist functions f: R --> R such that
$\displaystyle f(x) - f(-x) = x^2 $ for all $\displaystyle x \epsilon R?$
I've a hunch it's no, as any squared term would be the same under x and -x, but I'm not sure how to provide a formal proof.
Do there exist functions f: R --> R such that
$\displaystyle f(x) - f(-x) = x^2 $ for all $\displaystyle x \epsilon R?$
I've a hunch it's no, as any squared term would be the same under x and -x, but I'm not sure how to provide a formal proof.