Final answer:
The domain of the function f(x) = 4/(x-7) is all real numbers except for x = 7, because the function is undefined at x = 7 where the denominator would be zero.
Step-by-step explanation:
To determine the domain of the function f(x) = \frac{4}{x-7}, we need to consider the values of x for which the function is defined. The only restriction is that the denominator cannot be zero, as division by zero is undefined. Therefore, x cannot equal 7. The domain of the function is all real numbers except for x = 7.