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I am struggling with this problem:

 

(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 don't know where to start. So far, I've tried graphing these two functions and using the horizontal line test but I'm not confident with my answer.

 

Help would be appreciated.

 Mar 25, 2021
 #1
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Just graph the functions.  Then you can just use the Horizontal Line Test.

 Mar 25, 2021

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