Final answer:
The correct answer is A. x = 10 because it satisfies the condition for the domain of the square root function f(x) = √x - 8, which requires the expression under the square root to be non-negative.
Step-by-step explanation:
The question asks which value of x is in the domain of the function √x - 8. The domain of a function refers to the set of all possible input values (x values) that the function can accept. For the square root function, the domain includes all values of x for which the expression under the square root is non-negative (greater than or equal to zero). This means we are looking for an x value such that the expression under the square root, x - 8, is ≥ 0. Thus, solving the inequality x - 8 ≥ 0, we get x ≥ 8.
Now let's look at the options provided:
- A. x = 10: Plugging into the inequality, 10 - 8 ≥ 0, which is true, so this is in the domain.
- B. x = 7: For this value, 7 - 8 ≥ 0, which is false, hence not in the domain.
- C. x = 8: Here, 8 - 8 ≥ 0, this is true, making it a valid value in the domain.
- D. x = 0: This gives 0 - 8 ≥ 0, which is false, so this is not in the domain.
Therefore, the correct answer is A. x = 10, as it satisfies the condition for the domain of the function √x - 8.