Final answer:
x = 1 is not part of the domain of the function f(x) = √(x – 10) because plugging in x = 1 results in taking the square root of a negative number, which is not defined in the real numbers.
Step-by-step explanation:
The function rule given is f(x) = √(x – 10). To determine whether x = 1 is part of the domain of the function, we need to check if the expression under the square root is non-negative, as the square root of a negative number is not defined in the set of real numbers.
The expression inside the square root for x = 1 is (1 – 10), which equals -9. Since we cannot take the square root of a negative number in the real number system, x = 1 is not part of the domain of the function. In fact, for f(x) to be real, x must be greater than or equal to 10, which means the domain of the function f(x) is [10, ∞), where ∞ represents infinity.