Question

What is the domain of the function y = √x - 5?

1) negative infinity < x < infinity
2) 0 < x < infinity
3) 0 ≤ x < infinity
4) 1 ≤ x < infinity

Answer 1

The domain of the function y = √x - 5 is 5 ≤ x < infinity, as x must be equal to or greater than 5 to avoid taking the square root of a negative number.

Step-by-step explanation:

The domain of the function y = √x - 5 refers to the set of all possible x-values that can be substituted into the function without resulting in an undefined expression. Since the square root of a negative number is not a real number, x must be greater than or equal to 5 to ensure that the expression inside the square root is non-negative. Therefore, option 2) 0 < x < infinity is incorrect because it allows for x-values that result in a negative value under the square root when subtracting 5. The correct domain of the function is 5 ≤ x < infinity, which is not explicitly listed in the provided options.