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# Confused

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(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.

Mar 16, 2021