Final answer:
The correct answer is option A. The domain of the function f(x) = √x - 8 includes all x values for which x - 8 is non-negative. Upon solving the inequality x ≥ 8, we find that out of the given options, x = 10 is the only value that lies within the domain, making option A the correct choice.
Step-by-step explanation:
The student asked which value of x is in the domain of f(x) = √x - 8. The domain of a square root function includes all x values for which the expression under the square root is non-negative. This is because the square root of a negative number is not defined in the set of real numbers. Therefore, to find the domain, we need to solve the inequality x - 8 ≥ 0. Solving this inequality, we add 8 to both sides to get x ≥ 8.
Looking at the options provided:
- A. x = 10: This value is in the domain as 10 - 8 = 2, which is non-negative.
- B. x = 7: This value is not in the domain as 7 - 8 = -1, which is negative.
- C. x = 8: This value is exactly at the boundary of the domain, so it is included.
- D. x = 0: This value is not in the domain as 0 - 8 = -8, which is negative.
Therefore, the correct option is A. x = 10.