Functions

Hi, can someone help me with these two problems? (Please also explain how you got the answers)

1. Let $f(x) : (-\infty,0) \cup (0,\infty) \to \mathbb{R}$ be defined by f(x) = x - 1/x. Show that f(x) has no inverse function.

2. Let $g(x) : (0,\infty) \to \mathbb{R}$ be defined by g(x) = x - 1/x. Show that g(x) has an inverse function.

Thank you so much!