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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.

 

Could you show a way to prove this other than graphing? Thanks!

 Dec 21, 2021
 #1
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You can do this by using the horizontal line test.

 Dec 21, 2021
 #2
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How would you prove that using equations though?

Guest Dec 21, 2021

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