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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.

 

I know somebody already posted this. But how would you figure it out without plotting the graph of the function and instead do the work algebraically.

 Dec 30, 2021
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For these kinds of problems, you can just graph the function, then use the Horizontal Line Test.

 Dec 30, 2021

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