OSN 2015 Problem 4

Let function pair $f,g : \mathbb{R^+} \rightarrow \mathbb{R^+}$ satisfies $$f(g(x)y + f(x)) = (y+2015)f(x)$$ for every $x,y \in \mathbb{R^+}$ a. Prove that $f(x) = 2015g(x)$ for every $x \in \mathbb{R^+}$ b. Give an example of function pair $(f,g)$ that satisfies the statement above and $f(x), g(x) \geq 1$ for every $x \in \mathbb{R^+}$