# Thread: Existence of a function

1. ## Existence of a function

Do there exist functions f: R --> R such that

$f(x) - f(-x) = x^2$ for all $x \epsilon R?$

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.

2. Originally Posted by h2osprey
Do there exist functions f: R --> R such that
$f(x) - f(-x) = x^2$ for all $x \epsilon R?$
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.
If $g$ is any function on $\mathbb{R}$ and $h(x)=g(x)-g(-x)$ can you show that $h$ is an odd function?

3. Ah yes of course. Thanks!