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Question Number 6186 by sanusihammed last updated on 17/Jun/16
$${If}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:\:{and}\:\:{ff}\left({x}\right)\:=\:{x}\:+\:\mathrm{1}\: \\ $$$${then}\:{x}\:=\:? \\ $$
Commented by Rasheed Soomro last updated on 17/Jun/16
$${If}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:\:{and}\:\:{ff}\left({x}\right)\:=\:{x}\:+\:\mathrm{1}\: \\ $$$${then}\:{x}\:=\:? \\ $$$$−−−−−−−−− \\ $$$${f}\left({x}\right)=\mathrm{2}{x}\Rightarrow{f}\left(\:{f}\left({x}\right)\:\right)={f}\left(\mathrm{2}{x}\right)=\mathrm{2}\left(\mathrm{2}{x}\right)=\mathrm{4}{x}....\left({i}\right) \\ $$$${But}\:\:\:{f}\left(\:{f}\left({x}\right)\:\right)={x}+\mathrm{1}....\left({ii}\right) \\ $$$${From}\:\left({i}\right)\:\&\:\left({ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}{x}={x}+\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:{x}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$
Commented by sanusihammed last updated on 17/Jun/16
$${Thank}\:{you}\:{so}\:{much} \\ $$