Question 119
Find all pairs of functions $f, g : \mathbb{R} \to \mathbb{R}$ such that:
(1) $f(xg(y+1)) + y = x f(y) + f(x+g(y))$ for any two $x, y \in \mathbb{R}$;
(2) $f(0) + g(0) = 0$.
(1) $f(xg(y+1)) + y = x f(y) + f(x+g(y))$ for any two $x, y \in \mathbb{R}$;
(2) $f(0) + g(0) = 0$.