1. The problem asks for the domain of the function $f(x) = 3^{x-2}$. 2. The domain of a function is the set of all possible input values ($x$) for which the function is defined. 3. For exponential functions of the form $a^{x}$ where $a > 0$ and $a \neq 1$, the domain is all real numbers because you can raise a positive number to any real power. 4. Here, $f(x) = 3^{x-2}$ is an exponential function with base 3, which is positive and not equal to 1. 5. Therefore, the domain of $f(x)$ is all real numbers. 6. In set notation, this is written as $\{ x \mid x \text{ is a real number} \}$. Final answer: The domain of $f(x) = 3^{x-2}$ is $\{ x \mid x \text{ is a real number} \}$.