+87 (a) Let \(f(x) : (-\infty,0) \cup (0,\infty) \to \mathbb{R} \) be defined by \( f(x) = x - \frac{1}{x}.\)
Show that \(f(x)\) has no inverse function.
(b) Let \(g(x) : (0,\infty) \to \mathbb{R} \) be defined by \(g(x) = x - \frac{1}{x}.\)
Show that \(g(x)\) has an inverse function.
