Let $f : R\rightarrow R$ be a positive increasing function with $\lim\limits_{x\to 0}\large\frac{f(3x)}{f(x)}$$=1$. Then $\lim\limits_{x\to \infty}\large\frac{f(2x)}{f(x)}$ = ?

Question

$(a)\;\large\frac{2}{3}$$\qquad(b)\;\large\frac{3}{2}$$\qquad(c)\;3\qquad(d)\;1$