Final answer:
The domain of the function is all real numbers greater than 4, and the range is all real numbers.
Step-by-step explanation:
The domain of a logarithmic function is the set of all positive real numbers greater than zero, because the logarithm of a negative number or zero is undefined. For the function f(x) = log(x - 4) - 37, the value inside the logarithm must be greater than zero, so x - 4 > 0. Solving this inequality, we get x > 4.
Therefore, the domain of the function f(x) is all real numbers greater than 4. The range of a logarithmic function is the set of all possible output values. Since the logarithm of a positive number is always defined, there are no restrictions on the range. Therefore, the range of the function f(x) is all real numbers.