6. (51st Czech and Slovak Mathematical Olympiad (Final) Problem) Let $\mathrm{R}^{+}$ denote the set of positive real numbers. Find the function $f: \mathrm{R}^{+} \rightarrow \mathrm{R}^{+}$, such that for all $x, y \in \mathbf{R}$, we have $f(x f(y))=f(x y)+x$.