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Question Number 92438 by Ar Brandon last updated on 06/May/20

find the domaine and simplify  the function  f(x)=arcos(((1−x^2 )/(1+x^2 )))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{domaine}\:\mathrm{and}\:\mathrm{simplify} \\ $$$$\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{arcos}\left(\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right) \\ $$

Commented by Joel578 last updated on 07/May/20

g(x) = cos^(−1) (x) has domain −1 ≤ x ≤ 1, so  f(x) = cos^(−1) (((1 − x^2 )/(1 + x^2 ))) has domain x ∈ R

$${g}\left({x}\right)\:=\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right)\:\mathrm{has}\:\mathrm{domain}\:−\mathrm{1}\:\leqslant\:{x}\:\leqslant\:\mathrm{1},\:\mathrm{so} \\ $$$${f}\left({x}\right)\:=\:\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}\:−\:{x}^{\mathrm{2}} }{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\:\mathrm{has}\:\mathrm{domain}\:{x}\:\in\:\mathbb{R} \\ $$

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