The function \( f(x) = 3^x \) is an exponential function where the base \( 3 \) is a positive constant. The domain of an exponential function like this one is all real numbers. Therefore, the domain of \( f(x) = 3^x \) can be expressed in interval notation as:
\[ (-\infty, \infty) \]
This means that you can input any real number for \( x \) in the function.