Calculus, 10th Edition (Anton)

$\{ -3, -2, -1 , 1, 2,3 \}$
$g \circ f = g(f(x))$ We begin by examining the domain of $g(x)$ which is $\{ -3, -2, -1, 0 , 1, 2,3 \}$. Therefore, the domain of $g \circ f$ are all $x$ which $f(x)$ produces a value in the domain of $g$. Because the domain of $g$ is $\{ -3, -2, -1, 0 , 1, 2,3 \}$, the values of $x$ for which $f(x)$ produces such values are $\{ -3, -2, -1 , 1, 2,3 \}$. These values then form the domain of $g \ \circ f$.