1. The problem asks to find $g^2(x)$ when $g(x) = x - 3$. 2. The notation $g^2(x)$ means the function $g$ composed with itself: $g(g(x))$. 3. To find $g^2(x)$, substitute $g(x)$ into $g$: $$g^2(x) = g(g(x)) = g(x - 3)$$ 4. Since $g(t) = t - 3$ for any input $t$, replace $t$ with $x - 3$: $$g(x - 3) = (x - 3) - 3$$ 5. Simplify the expression: $$g^2(x) = x - 3 - 3 = x - 6$$ 6. Therefore, the function $g^2(x)$ is: $$g^2(x) = x - 6$$