To find the domain of the function $f(x) = \sqrt{x - 3}$, we need to ensure that the expression inside the square root is non-negative. This is because the square root of a negative number is not defined in the set of real numbers.

Therefore, the inequality that must hold is: $x - 3 \geq 0$

This inequality ensures that $x - 3$ is greater than or equal to zero, which makes the square root expression valid for real numbers.

Answer: $x - 3 \geq 0$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you find the domain of a function involving a square root?
2. What is the domain of $f(x) = \sqrt{x + 2}$?
3. Can a square root function ever produce negative numbers as output?
4. How would the domain change if the function were $f(x) = \sqrt{-x + 3}$?
5. What are the general rules for finding domains of functions involving square roots?

Tip: To find the domain of functions with radicals, always look for the condition that makes the expression inside the radical non-negative.