To determine the domain of the function [tex]\( f(x) = \sqrt{x-3} \)[/tex], we need to ensure that the expression inside the square root is non-negative. In other words, the value inside the square root must be greater than or equal to zero. This is because the square root of a negative number is not defined in the set of real numbers.
So, we set up the inequality for the expression inside the square root:
[tex]\[ x - 3 \geq 0 \][/tex]
This inequality ensures that the value under the square root is non-negative, making the function [tex]\( f(x) = \sqrt{x-3} \)[/tex] defined.
Among the choices given:
- [tex]\(\sqrt{x-3} \geq 0\)[/tex] is not the correct inequality to determine the domain.
- [tex]\(\sqrt{x-3} \leq 0\)[/tex] and [tex]\(x-3 \leq 0\)[/tex] are also not relevant to defining when the expression inside the square root is non-negative.
Therefore, the correct inequality to find the domain of [tex]\( f(x) = \sqrt{x-3} \)[/tex] is:
[tex]\[ x-3 \geq 0. \][/tex]
