Final answer:
The value of x that is in the domain of the function f(x) = √(x – 8) is A. x = 10, as it is the only option that results in a non-negative number inside the square root.
Step-by-step explanation:
The question pertains to identifying which value of x is within the domain of the function f(x) = √(x – 8). The domain of a square root function includes all values of x for which the expression inside the square root is non-negative since the square root of a negative number is not defined in the set of real numbers. Therefore, x must be greater than or equal to 8 for the function to be real-valued.
Let's evaluate the options provided:
- A. x = 10: This is in the domain because 10 - 8 = 2, and the square root of 2 is a real number.
- B. x = 7: This is not in the domain because 7 - 8 = -1, and the square root of -1 is not a real number.
- C. x = –8: This is not in the domain because -8 - 8 = -16, and the square root of -16 is not a real number.
- D. x = 0: This is not in the domain because 0 - 8 = -8, and the square root of -8 is not a real number.
Therefore, the correct answer is A. x = 10, which is the value within the domain of the function f(x).