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Question Number 165160 by mathlove last updated on 26/Jan/22
$${f}\left({x}+{f}\left({x}\right)\right)=\mathrm{3}{f}\left({x}\right)\:\:\:{and}\:{f}\left(−\mathrm{1}\right)=\mathrm{7} \\ $$$${faind}\:\:{f}\left(\mathrm{27}\right)=? \\ $$
Answered by Rasheed.Sindhi last updated on 26/Jan/22
$${x}=−\mathrm{1}:\:{f}\left(−\mathrm{1}+{f}\left(−\mathrm{1}\right)\right)=\mathrm{3}{f}\left(−\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:{f}\left(−\mathrm{1}+\mathrm{7}\right)=\mathrm{3}\left(\mathrm{7}\right) \\ $$$$\:\:\:\:\:\:{f}\left(\mathrm{6}\right)=\mathrm{21} \\ $$$${x}=\mathrm{6}:{f}\left(\mathrm{6}+{f}\left(\mathrm{6}\right)\right)=\mathrm{3}{f}\left(\mathrm{6}\right) \\ $$$$\:\:\:\:\Rightarrow{f}\left(\mathrm{6}+\mathrm{21}\right)=\mathrm{3}\left(\mathrm{21}\right)=\mathrm{63} \\ $$$$\:\:\:\Rightarrow{f}\left(\mathrm{27}\right)=\mathrm{63} \\ $$