Question Number 212711 by RojaTaniya last updated on 21/Oct/24
$$\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}−{x}} \\ $$$$\:{y}={f}\left({x}\right),\:{z}={f}\left({y}\right),\:{f}\left({z}\right)=? \\ $$
Answered by MATHEMATICSAM last updated on 21/Oct/24
$${y}\:=\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}\:−\:{x}} \\ $$$${f}\left({y}\right)\:=\:{f}\left(\frac{\mathrm{1}}{\mathrm{1}\:−\:{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{1}\:−\:{x}}}\:=\:\frac{\mathrm{1}\:−\:{x}}{−\:{x}}\:=\:\frac{{x}\:−\:\mathrm{1}}{{x}} \\ $$$${z}\:=\:{f}\left({y}\right)\:=\:\frac{{x}\:−\:\mathrm{1}}{{x}} \\ $$$${f}\left({z}\right)\:=\:{f}\left(\frac{{x}\:−\:\mathrm{1}}{{x}}\right)\:=\:\:\frac{\mathrm{1}}{\mathrm{1}\:−\:\frac{{x}\:−\:\mathrm{1}}{{x}}}\:=\:{x} \\ $$