(a) Let $f : (-\infty,0) \cup (0,\infty) \to \mathbb{R}$ be defined by
\[f(x) = x - \frac{1}{x}.\]Show that $f$ has no inverse function.
(b) Let $g : (0,\infty) \to \mathbb{R}$ be defined by
\[g(x) = x - \frac{1}{x}.\]Show that $g$ has an inverse function.
Could you show a way to prove this other than graphing? Thanks!
