Let-f-R-R-be-a-function-satisfying-the-relation-f-x-f-y-f-xy-x-for-all-x-y-R-Then-lim-x-0-f-x-1-3-1-f-x-1-2-1-A-1-

Question Number 186748 by EnterUsername last updated on 09/Feb/23

Let f : R^{+} \to R^{+} be a function satisfying the relation

f (x . f (y)) = f (x y) + x for all x, y \in R^{+} . Then

\lim_{x \to 0} (\frac{{(f (x))}^{1 / 3} - 1}{{(f (x))}^{1 / 2} - 1}) =

(A) 1 (B) \frac{1}{2}

(C) \frac{2}{3} (D) \frac{3}{2}