VMO 2003 Problem 6

Let $R^+$ be the set of positive reals and let F be the set of all functions f : $R^+$ → $R^+$ such that f(3x) ≥ f( f(2x) ) + x for all x. Find the largest A such that f(x) ≥ A x for all f in F and all x in $R^+$.