1. **State the problem:** We are given two functions $f(x) = x + 3$ and $g(x) = x - 1$. We need to find the product of these functions, denoted as $(f \cdot g)(x)$, and simplify the result. 2. **Formula used:** The product of two functions $f$ and $g$ is defined as: $$ (f \cdot g)(x) = f(x) \times g(x) $$ This means we multiply the expressions for $f(x)$ and $g(x)$. 3. **Apply the formula:** Substitute the given functions: $$ (f \cdot g)(x) = (x + 3)(x - 1) $$ 4. **Simplify the expression:** Use the distributive property (FOIL method) to expand: $$ (x + 3)(x - 1) = x \times x + x \times (-1) + 3 \times x + 3 \times (-1) $$ $$ = x^2 - x + 3x - 3 $$ $$ = x^2 + 2x - 3 $$ 5. **Final answer:** The simplified product of the functions is: $$ (f \cdot g)(x) = x^2 + 2x - 3 $$