Find the domain of the function. \[ f(x)=\log _{9}(x-4) \] The domain of \( f \) is \( \square \). (Type your answer in interval notation.)

To find the domain of the function \( f(x)=\log _{9}(x-4) \), we need to determine when the argument of the logarithm, \( x-4 \), is positive. Thus, we set up the inequality: \[ x - 4 > 0 \] Solving this gives: \[ x > 4 \] This means that the function is defined for all \( x \) greater than 4. In interval notation, the domain of \( f \) is: \[ (4, \infty) \] To clarify, this means any value greater than 4 can be plugged into the function without running into the pesky issue of taking the logarithm of a non-positive number. So, feel free to dance around those numbers greater than 4 without any worries!