Do you mean explain why f(g(x)) exists but g(f(x)) does not?

f(g(x)) exists if the range of g is a subset of the domain of f. The range of g is all real numbers. This is a subset of the domain of f. Therefore f(g(x)) exists.

Note: Any set is considered a subset of itself.

g(f(x)) exists if the range of f is a subset of the domain of g. The range of f is all real numbers greater than OR EQUAL TO zero. This is NOT a subset of the domain of g because the domain of g does NOT include zero. Therefore g(f(x)) does not exist.