JEE Main 2022 (Online) 26th July Morning ShiftQuestion 1
Let $f:\mathbf{R}\to\mathbf{R}$ be a continuous function such that $f(3x)-f(x)=x$. If $f(8)=7$, then $f(14)$ is equal to :
Limits & Continuity
Solution
$f(x)=f(x/3)+x/3=f(x/9)+x/9+x/3=\dots=f(x/3^n)+\frac x3\cdot\frac{1}{1-1/3}$. By continuity, $f(x)=f(0)+\frac x2$. $f(8)=f(0)+4=7\Rightarrow f(0)=3$. $f(14)=3+7=10$. Option (B).