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

This leads us to the inequality: $x - 3 \geq 0$ Therefore, the correct inequality is: $x - 3 \geq 0$ This ensures that $x \geq 3$, which is the domain of the function $f(x) = \sqrt{x - 3}$.

Answer: $x - 3 \geq 0$

Would you like further details on domain restrictions or have any other questions?

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Here are 5 relative questions to expand on this topic:

1. What is the range of the function $f(x) = \sqrt{x - 3}$?
2. How do you determine the domain of a function involving both square roots and fractions?
3. What happens to the domain if the square root function had a negative sign, such as $f(x) = -\sqrt{x - 3}$?
4. How would the domain change if the function were $f(x) = \sqrt{3 - x}$ instead?
5. Can square root functions have negative values as outputs?

Tip: Always check for restrictions (like non-negative radicands or non-zero denominators) when determining the domain of a function.