Answer
We start with the domain of $g$ and find the subset of this domain that produces a range in the domain of $f$.
Work Step by Step
We know that $f \circ g =f(g(x))$. We also know that the domain is essentially "everything that $x$ is allowed to be" for a function (so that we get a real value for $y$). To find the domain of $f \circ g$, we start with the domain of $g$ (so that g(x) evaluates correctly). Then we find the values of $x$ in the domain of $g$ that produce a $g(x)$ that is in the domain of $f$. Thus we start with the domain of $g$ and find the subset of this domain that produces a range in the domain of $f$.
