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The question asks to determine the domain of the function \( f(x) = \sqrt{3x - 9} \). To find the domain, we must ensure that the expression under the square root is non-negative, as the square root function is only defined for non-negative numbers (i.e., the radicand must be greater than or equal to zero).

So, we set up the inequality:

\[
3x - 9 \geq 0
\]

Now, solve for \( x \):

\[
3x \geq 9
\]

\[
x \geq \frac{9}{3} = 3
\]

Therefore, the domain of the function is:

\[
x \geq 3
\]

The domain in interval notation is:

\[
[3, \infty)
\]

Would you like more details or have any further questions on this? 

Here are five related questions for further exploration:
1. How would the domain change if the function were \( f(x) = \sqrt{5x - 2} \)?
2. What is the range of \( f(x) = \sqrt{3x - 9} \)?
3. How would you graph \( f(x) = \sqrt{3x - 9} \)?
4. What happens to the domain if a negative square root is involved, e.g., \( f(x) = -\sqrt{3x - 9} \)?
5. How do you determine the domain of a rational function involving a square root?

**Tip:** For any function involving a square root, always check that the expression inside the root is non-negative to find the domain.

Determine the values of x that are in the domain of the function f(x) = √(3x - 9). Graph the solution.

Learn how to determine the domain of the function f(x) = √(3x - 9). This step-by-step solution explains how to ensure that the radicand is non-negative and solve the inequality 3x - 9 ≥ 0 to find the valid values of x. Suitable for students in Grades 9-11.

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