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Given-f-xy-f-x-y-and-f-7-7-find-f-1008-




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

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