1. The problem states that $f$ and $g$ are polynomial functions. 2. The domain of $\frac{f}{g}$ is $\mathbb{R} - \{3\}$, meaning $g(x) \neq 0$ for all $x \neq 3$, and $g(3) = 0$. 3. The domain of $\frac{g}{f}$ is $\mathbb{R} - \{2\}$, meaning $f(x) \neq 0$ for all $x \neq 2$, and $f(2) = 0$. 4. Since $f$ and $g$ are polynomials, they are defined for all real numbers, so their individual domains are $\mathbb{R}$. 5. The domain of the product $f \cdot g$ is the intersection of the domains of $f$ and $g$, which is $\mathbb{R}$ because polynomials are defined everywhere. 6. There are no restrictions on the domain of $f \cdot g$ from zeros of denominators since it is a product, not a quotient. 7. Therefore, the domain of $f \cdot g$ is $\mathbb{R}$. **Final answer:** (a) $\mathbb{R}$