Question Number 167750 by mathlove last updated on 24/Mar/22
Answered by Rasheed.Sindhi last updated on 24/Mar/22
$${f}\left({x}−{y}\right)={f}\left({x}\right)−{f}\left({y}\right);\:{f}\left(\mathrm{2}\right)=\mathrm{5};\:{f}\left(\mathrm{16}\right)=? \\ $$$$\bullet{x}=\mathrm{2}{y} \\ $$$${f}\left(\mathrm{2}{y}−{y}\right)={f}\left(\mathrm{2}{y}\right)−{f}\left({y}\right) \\ $$$${f}\left({y}\right)={f}\left(\mathrm{2}{y}\right)−{f}\left({y}\right) \\ $$$$\mathrm{2}{f}\left({y}\right)={f}\left(\mathrm{2}{y}\right) \\ $$$$\bullet\mathrm{2}{y}={x}\Rightarrow{y}=\frac{{x}}{\mathrm{2}} \\ $$$${f}\left({x}\right)=\mathrm{2}{f}\left(\frac{{x}}{\mathrm{2}}\right) \\ $$$${f}\left(\mathrm{16}\right)=\mathrm{2}{f}\left(\mathrm{8}\right)=\mathrm{2}×\mathrm{2}{f}\left(\mathrm{4}\right)=\mathrm{2}×\mathrm{2}×\mathrm{2}{f}\left(\mathrm{2}\right) \\ $$$$=\mathrm{8}×\mathrm{5}=\mathrm{40} \\ $$