Question Number 217015 by hardmath last updated on 26/Feb/25
$$\mathrm{If} \\ $$$$\mathrm{f}\left(\mathrm{2x}\:+\:\mathrm{1}\right)\:=\:\mathrm{3x}\:+\:\mathrm{5} \\ $$$$\mathrm{Find} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$
Answered by Rasheed.Sindhi last updated on 26/Feb/25
$${let}\:\mathrm{2x}+\mathrm{1}=\mathrm{y} \\ $$$$\:\:\:\:\:\:\:\mathrm{x}=\frac{\mathrm{y}−\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{f}\left(\mathrm{y}\right)=\mathrm{3}\left(\frac{\mathrm{y}−\mathrm{1}}{\mathrm{2}}\right)+\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:=\frac{\mathrm{3y}−\mathrm{3}+\mathrm{10}}{\mathrm{2}} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{3x}+\mathrm{7}}{\mathrm{2}} \\ $$
Answered by Hanuda354 last updated on 27/Feb/25
$${f}\left(\mathrm{2}{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{3}{x}\:+\:\mathrm{5} \\ $$$${f}\left(\mathrm{2}{x}\:+\:\mathrm{1}\right)\:=\:\frac{\mathrm{3}}{\mathrm{2}}\left(\mathrm{2}{x}+\mathrm{1}\right)+\frac{\mathrm{7}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:{x}\:+\:\frac{\mathrm{7}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)\:=\:\frac{\mathrm{3}{x}\:+\:\mathrm{7}}{\mathrm{2}} \\ $$