Question Number 117577 by ZiYangLee last updated on 12/Oct/20
$$\mathrm{If}\:{f}\left({x}\right),\:{g}\left({x}\right)\:\mathrm{and}\:{h}\left({x}\right)\:\mathrm{are}\:\mathrm{three}\:\mathrm{functions}, \\ $$$$\mathrm{where}\:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{5}} −\mathrm{8}{x}^{\mathrm{2}} +\mathrm{1},\:{f}\left({x}−\mathrm{3}\right)={g}\left(\mathrm{3}{x}−\mathrm{2}\right) \\ $$$$\mathrm{and}\:{g}\left(\mathrm{3}{x}+\mathrm{1}\right)={h}\left({x}+\mathrm{3}\right),\:\mathrm{show}\:{h}\left({x}\right)={f}\left({x}−\mathrm{5}\right). \\ $$
Answered by Olaf last updated on 12/Oct/20
$${h}\left({x}\right)\:=\:{g}\left(\mathrm{3}\left({x}−\mathrm{3}\right)+\mathrm{1}\right)\:=\:{g}\left(\mathrm{3}\left({x}−\mathrm{2}\right)−\mathrm{2}\right) \\ $$$$=\:{f}\left(\left({x}−\mathrm{2}\right)−\mathrm{3}\right)\:=\:{f}\left({x}−\mathrm{5}\right) \\ $$
Commented by ZiYangLee last updated on 12/Oct/20
$$\mathrm{hmmm}.. \\ $$