Question 1
Determine all pairs $(f, g)$ of functions $f, g: \mathbb{R} \rightarrow \mathbb{R}$ such that for all $x, y \in \mathbb{R}$
- $f(x) \geq 0$,
- $f(x+g(y))=f(x)+f(y)+2 y g(x)-f(y-g(y))$.
- $f(x) \geq 0$,
- $f(x+g(y))=f(x)+f(y)+2 y g(x)-f(y-g(y))$.