Question Number 94318 by john santu last updated on 18/May/20
$$\mathrm{Given}\:\mathrm{f}\left(\mathrm{xy}\right)\:=\:\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\:\mathrm{and}\: \\ $$$$\mathrm{f}\left(\mathrm{7}\right)\:=\:\mathrm{7}.\:\mathrm{find}\:\mathrm{f}\left(\mathrm{1008}\right)\: \\ $$
Commented by Rasheed.Sindhi last updated on 18/May/20
$${f}\left(\mathrm{7}\right)={f}\left(\mathrm{7}×\mathrm{1}\right)={f}\left(\mathrm{7}+\mathrm{1}\right)=\mathrm{7} \\ $$$${f}\left(\mathrm{8}\right)=\mathrm{7} \\ $$$${f}\left(\mathrm{8}\right)={f}\left(\mathrm{8}×\mathrm{1}\right)={f}\left(\mathrm{8}+\mathrm{1}\right)=\mathrm{7} \\ $$$${f}\left(\mathrm{9}\right)=\mathrm{7} \\ $$$${f}\left({x}\right)={f}\left({x}×\mathrm{1}\right)={f}\left({x}+\mathrm{1}\right) \\ $$$${f}\left({x}+\mathrm{1}\right)={f}\left({x}\right) \\ $$$$\therefore{f}\left(\mathrm{1008}\right)=\mathrm{7} \\ $$
Commented by john santu last updated on 18/May/20
$$\mathrm{yes}….\mathrm{i}\:\mathrm{agree}\: \\ $$