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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
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Just plot the graph, and use the Horizontal Line Test.

 Mar 16, 2021

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