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# Urgent Function Help!!

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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

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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