Question Number 186769 by naka3546 last updated on 10/Feb/23
$$\mathrm{Given}\:\:\mathrm{function}\:\:\:{f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R}\:\:\:\mathrm{satisfy}\:\:\mathrm{that} \\ $$$$\:\:\:\:\left({f}\:\circ\:{f}\right)\left({x}\right)\:+\:{x}\:=\:\left({x}+\mathrm{1}\right)\:{f}\left({x}\right)\:. \\ $$$$\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{value}\:\:\mathrm{of}\:\:{f}\left(\mathrm{1}\right)\:. \\ $$