If f (x) = StartRoot x minus 3 EndRoot, which inequality can be used to find the domain of f(x)?
StartRoot x minus 3 EndRoot greater-than-or-equal-to 0
x minus 3 greater-than-or-equal-to 0
StartRoot x minus 3 EndRoot less-than-or-equal-to 0
x minus 3 less-than-or-equal-to 0

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.

If f(x) = √(x - 3), which inequality can be used to find the domain of f(x)? √(x - 3) ≥ 0, x - 3 ≥ 0, √(x - 3) ≤ 0, or x - 3 ≤ 0

Learn how to find the domain of the function f(x) = √(x - 3) by solving the inequality x - 3 ≥ 0. This problem covers key algebraic concepts including the domain of functions involving square roots. Suitable for students in Grades 9-11.

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