Final answer:
The correct value of x that is in the domain of the function f(x) = √x - 7 is x = 8, since it is the only option given that does not result in a negative number under the square root, ensuring it is part of the domain of the function.
Step-by-step explanation:
The value of x that is in the domain of the function f(x) = √x - 7 must make the expression under the square root non-negative since the square root of a negative number is not defined in the set of real numbers. In other words, we are looking for a value of x where x - 7 ≥ 0.
When we apply this to the given options, we find:
Option A: x = 8 makes 8 - 7 = 1, which is non-negative.
Option B: x = -3 makes -3 - 7 = -10, which is negative and therefore not in the domain.
Option C: x = 6 makes 6 - 7 = -1, which is negative and therefore not in the domain.
Option D: x = 0 makes 0 - 7 = -7, which is negative and therefore not in the domain.
Therefore, the correct value of x in the domain of this function is x = 8 (Option A).