Problem

Source: Iran TST 2013:TST 2,Day 1,Problem 3

Tags: function, algebra proposed, algebra



find all functions $f,g:\mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ such that $f$ is increasing and also: $f(f(x)+2g(x)+3f(y))=g(x)+2f(x)+3g(y)$ $g(f(x)+y+g(y))=2x-g(x)+f(y)+y$