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 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.

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

Discover how to find the domain of the square root function f(x) = √(x - 3). This detailed solution explains why the inequality x - 3 ≥ 0 determines the domain and provides key insights into the behavior of square root functions. Suitable for Grades 8-10 students.

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