Question

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

• A. 4
• B. 10
• C. 11
• D. 16

Answer 1

Answer: (B)

$ f(x)-f(x / 3)=x / 3$
$ f(x / 3)-f\left(x / 3^2\right)=x / 3^2$
.... on adding
$f(x)-\displaystyle\lim _{n \rightarrow \infty} f\left(\frac{x}{3^n}\right)=x\left(\frac{1}{3}+\frac{1}{3^2} \ldots \infty\right) $
$ f(x)-f(0)=\frac{x}{2}$
$ f(8)=7 ; f(0)=3 $
$ f(x)=x / 2+3 $
$ f(14)=10$