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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.

 

Thanks in advance

 Dec 30, 2021
 #1
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You can just plot the graphs, and apply the Horizontal Line Test.  The graphs make it obvious.

 Dec 30, 2021
 #2
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But how would you do it algebraically without graphing to find if there is or if there is not an inverse

 Dec 30, 2021

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