1. The problem asks for the domain of the function $f(x) = 3^{x-2}$. 2. The domain of an exponential function $a^x$ where $a > 0$ and $a \neq 1$ is all real numbers because you can raise a positive base to any real exponent. 3. Here, the base is 3, which is positive and not equal to 1, so the domain is all real numbers. 4. Therefore, the domain of $f(x) = 3^{x-2}$ is $\{x \mid x \text{ is a real number}\}$.