To determine the domain of the function [tex]\( f(x) = \sqrt{x-3} \)[/tex], let's analyze the conditions under which the expression inside the square root is valid.
We know that the square root function is only defined for non-negative values. Therefore, the expression inside the square root, namely [tex]\( x - 3 \)[/tex], must be non-negative.
1. Identify the requirement for the square root:
[tex]\[
x - 3 \geq 0
\][/tex]
2. Solve the inequality:
To solve the inequality [tex]\( x - 3 \geq 0 \)[/tex]:
[tex]\[
x \geq 3
\][/tex]
This inequality represents the domain of the function [tex]\( f(x) = \sqrt{x-3} \)[/tex].
Hence, the correct inequality from the given options that can be used to find the domain of [tex]\( f(x) \)[/tex] is:
[tex]\[ x - 3 \geq 0 \][/tex]
Which corresponds to the second choice in the given list.
[tex]\[
\boxed{x-3 \geq 0}
\][/tex]
