1. (Easy) Define $f(x)=x^{2}-x-4$ and $g(x)=\log _{2}(x-2)$. Find the domain of $g \circ f$.
Answer: $(-\infty,-2) \cup(3,+\infty)$.
Solution: Note first that we need $f(x)>2$ so that $g \circ f$ is defined. Hence, we have $x^{2}-x-4>2$, or $x^{2}-x-6>0$. This factors into $(x+2)(x-3)>0$, and quick interval testing shows that the intervals $(-\infty,-2)$ and $(3,+\infty)$ are the ones that work. (A table of signs may also be used.)