(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show tan(x): (-pi/2, pi/2) -> R has a continuous inverse arctan(x) : R -> (-pi/2, pi/2).

You may assume that tan(x) is continuous and strictly increasing on the given domain, and tends to +/- [tex]\infty[/tex] at +/- pi/2

2. Relevant equations

3. The attempt at a solution

I think I have shown that tan(x) has an inverse on this domain by showing it is bijective.

However, I am unsure how to go about showing that arctan(x) is continuous.

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# Show that arctan(x) exists and is continuous

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