Let $f,g:\mathbb R \to \mathbb R$. Let $h_1$ = $f-g$ and $h_2$ = $f+g$. Suppose $h_1$ and $h_2$ are bounded. Show that $f$ and $g$ are bounded.
I understand the concept of bounded but would've thought you would need to use limits or a derivative to do a proof. How would you accomplish this without one.