Question Number 225330 by mathlove last updated on 21/Oct/25
$${if}\:\:\left({fogoh}\right)\left({x}\right)={cos}^{\mathrm{2}} \left({x}+\mathrm{9}\right) \\ $$$${then}\:\:\:{f}\left({x}\right)=?\:,\:\:{g}\left({x}\right)=?\:\:,\:{h}\left({x}\right)=? \\ $$
Answered by Raphael254 last updated on 21/Oct/25
$$ \\ $$$${f}\left({g}\left({h}\left({x}\right)\right)\right)\:=\:{cos}^{\mathrm{2}} \left({x}+\mathrm{9}\right) \\ $$$$ \\ $$$${f}\left({g}\left({x}\right)\right)\:=\:{cos}^{\mathrm{2}} \left({x}+\mathrm{9}\right) \\ $$$$ \\ $$$${f}\left({x}\right)\:=\:{cos}^{\mathrm{2}} \:{x} \\ $$$$ \\ $$$${g}\left({x}\right)\:=\:{x}+\mathrm{9} \\ $$$$ \\ $$$${h}\left({x}\right)\:=\:{x} \\ $$$$ \\ $$$${or} \\ $$$$ \\ $$$${f}\left({x}\right)\:=\:{x} \\ $$$$ \\ $$$${g}\left({x}\right)\:=\:{cos}^{\mathrm{2}} \:{x} \\ $$$$ \\ $$$${h}\left({x}\right)\:=\:{x}\:+\:\mathrm{9} \\ $$$$ \\ $$$${or} \\ $$$$ \\ $$$${f}\left({x}\right)\:=\:{x}^{\mathrm{2}} \\ $$$$ \\ $$$${g}\left({x}\right)\:=\:{x} \\ $$$$ \\ $$$${h}\left({x}\right)\:=\:{cos}\:{x} \\ $$$$ \\ $$$$… \\ $$