How can $G(x,y)=e^x-e^{-y} $ be written as $G(x_1,\dots,x_n)= F(\sum_{i=1}^n g_i(x_i))$?

Question

where $G$ is a real valued function defined on a convex region of Euclidean n-space, $g_i$ are real continuous functions, and $F$ is a strictly increasing real function?

Basically, I want to know what $F$, $g_i$ should be such that $G(x,y)= e^x-e^{-y} = F( \sum_{i=1}^n g_i(x_i))$

I'm particularly confused because, if $F$ is a function of $\sum_{i=1}^n g_i(x_i)$, then how are $x$ and $y$ appearing in separate terms (instead of as a sum)

Answer 1

Let $F(x) = x, g_1(x) = e^x, g_2(y) = -e^y$