1. **State the problem:** We are given two functions $f(x) = x + 3$ and $g(x) = x - 1$. We need to find the composite function $(fg)(x)$, which means $f(g(x))$. 2. **Formula and explanation:** The composite function $(fg)(x)$ is defined as $f(g(x))$. This means we substitute the entire function $g(x)$ into every $x$ in $f(x)$. 3. **Substitute $g(x)$ into $f(x)$:** $$ (fg)(x) = f(g(x)) = f(x - 1) $$ Since $f(x) = x + 3$, replace $x$ with $x - 1$: $$ f(x - 1) = (x - 1) + 3 $$ 4. **Simplify the expression:** $$ (x - 1) + 3 = x - 1 + 3 = x + 2 $$ 5. **Final answer:** $$(fg)(x) = x + 2$$ This means the composite function adds 2 to the input $x$ after applying $g(x)$ first.