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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'm really sorry this is last minute for asking for a thorough explanation, but I just got back from the hospital and my homework that I was supposed to do is  a lot, so it would be really great if someone could try and do this quickly :(

thank you so much in advance!! <3

 Feb 22, 2022
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Here is the graph of them

The original function is green and the inverse is orange.

Doesn't look to me like the inverse is a function either way ......

 

 

 Feb 22, 2022

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