(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.
I know somebody already posted this. But how would you figure it out without plotting the graph of the function and instead do the work algebraically.
