Consider the map $f:\mathbb{R}^n \times \mathbb{R}^n \rightarrow \mathbb{R}^n$. When is it the case that there exist functions $g:\mathbb{R}^n \rightarrow \mathbb{R}^n$ and $h:\mathbb{R}^n \rightarrow \mathbb{R}^n$ such that $\forall x,y\in\mathbb{R}^n$, $f(x,y)=g(x)+h(y)$?
Thank you!