Question

Let $f : R \rightarrow R$ be a continuous function such that $f (3x)- f(x)= x$. If $f(8)=7$, then $f (14)$ is equal to :

• A. 4
• B. 10
• C. 11
• D. 16

Answer 1

Answer: (B)

10

Answer 2

The correct option is (B) : 10
$f(x)-f(\frac{x}{3})=\frac{x}{3}$
$f(\frac{x}{3})-f(\frac{x}{3^2})=\frac{x}{3^2}$
By adding this …...
$f(x)-\lim\limits_{n\rightarrow\infty}f(\frac{x}{3^n})=x(\frac{1}{3}+\frac{1}{3^2}.....\infty)$
$f(x)-f(0)=\frac{x}{2}$
$f(8)=7;f(0)=3$
$f(x)=\frac{x}{2}+3$
$f(14)=10$