Question Number 145093 by mathdanisur last updated on 02/Jul/21
$${if}\:\:{f}\left({ax}+\mathrm{2}{b}\right)={x}\:\:{and}\:\:{f}\left(\mathrm{2}{a}\right)=\frac{{b}}{{a}} \\ $$$${find}\:\:{f}\left(\mathrm{5}{b}\right)=? \\ $$
Answered by liberty last updated on 02/Jul/21
$$\Leftrightarrow{f}\left({x}\right)=\frac{{x}−\mathrm{2}{b}}{{a}}\:\wedge\:{f}\left(\mathrm{2}{a}\right)=\frac{{b}}{{a}} \\ $$$$\Rightarrow\frac{\mathrm{2}{a}−\mathrm{2}{b}}{{a}}\:=\:\frac{{b}}{{a}}\:;\:\mathrm{3}{b}=\mathrm{2}{a}\:\&\:{a}=\frac{\mathrm{3}{b}}{\mathrm{2}} \\ $$$${then}\:{we}\:{get}\:{f}\left({x}\right)=\frac{\mathrm{2}\left({x}−\mathrm{2}{b}\right)}{\mathrm{3}{b}} \\ $$$${so}\:{f}\left(\mathrm{5}{b}\right)=\frac{\mathrm{2}\left(\mathrm{5}{b}−\mathrm{2}{b}\right)}{\mathrm{3}{b}}\:=\:\mathrm{2} \\ $$
Commented by mathdanisur last updated on 02/Jul/21
$${Cool}\:{Ser},\:{thank}\:{you} \\ $$