Final answer:
The domain of the given function f(x) is determined by the inequality x ≥ 2, ensuring the expression under the square root is non-negative. Due to a potential typo, none of the options provided match exactly, with option (c) x ≥ 20 being the closest under the assumption of a different function expression.
Step-by-step explanation:
To determine the domain of the function f(x) = √(5x - 10) - 10 + 3, we must consider when the expression under the square root is non-negative, since the square root of a negative number is not a real number. The inequality that represents the domain is therefore 5x - 10 ≥ 0, which simplifies to x ≥ 2. However, after reviewing the options provided, none matches this result. There may be a typo in the original function or the provided options. Nonetheless, if we adhere to the options given, the closest would be (c) x ≥ 20, but this assumes that the original function expression might have had a typo and should have been √(5x - 100).