Final answer:
The domain of the function f(x) = 9/(x-6) is all real numbers except x = 6.
Step-by-step explanation:
The domain of a function represents the set of all possible input values for which the function is defined. In this case, the function is f(x) = 9/(x-6). To determine the domain, we need to consider the values of x that make the denominator of the fraction equal to zero, since division by zero is undefined. So, we set x-6 = 0 and solve for x. This gives us x = 6. Therefore, the domain of f(x) is all real numbers except x = 6.