If $f(x) = (x+x)$ and $g(x) = 2(x-5)$, and we have the compound function $g(f(x))$, how can we "define what the resulting function does"?
It's obvious what is happening, but I'm not quite sure how this question is asking and how it would be laid out.
Perhaps, $g(x) = 2((x+x)-5)$
What the resulting function does is that it maps $f(x)\to \mathbb{R}$, that is, the new function, called a "composition of two functions", has the range of a function as its domain. Other than that, it retains all other functional properties of itself.
In this case, $g(f(x))$ maps from $f(x)\to \mathbb{R}$, so it has the range of $f(x)$ as its domain. And the function hence gets modified in a similar fashion. Since $g(x) = 2(x-5)$, so by logic, we conclude that $g(f(x)) = 2[f(x)-5] = 2[(x+x)-5]$.