The function given is:

$f(x) = \sqrt{x - 3} - 3$

Finding the Domain

Since the function contains a square root, the expression inside the square root $x - 3$ must be non-negative (greater than or equal to 0).

$x - 3 \geq 0$

$x \geq 3$

Thus, the domain of the function is all real numbers $x$ such that $x \geq 3$.

Domain in Interval Notation:

$[3, \infty)$

This means the function is only defined for values starting from $x = 3$ and going to infinity.

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Related Questions:

1. What is the range of the function $f(x) = \sqrt{x - 3} - 3$?
2. How do square root functions behave for negative inputs?
3. How do you determine domain for more complex functions with multiple constraints?
4. What changes if the function were $f(x) = \sqrt{3 - x} - 3$?
5. How does a graphing calculator verify the domain of a function?

Tip: When working with square roots, always start by ensuring the expression inside the radical is non-negative to find the domain.