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We are given the function \( f(x) = \sqrt{x^2 - 9} \) and need to determine its domain, or the set of possible values for \( x \).

To ensure the function is defined, the expression under the square root must be non-negative:

\[
x^2 - 9 \geq 0
\]

This simplifies to:

\[
x^2 \geq 9
\]

Next, solving this inequality:

\[
x \geq 3 \quad \text{or} \quad x \leq -3
\]

Thus, the domain of the function \( f(x) \) is:

\[
x \in (-\infty, -3] \cup [3, \infty)
\]

This corresponds to option **e** in the provided choices:

\[
\{ x \,|\, x \leq -9 \, \text{or} \, x \geq 3, x \in \mathbb{R} \}
\]

Would you like further explanation or have any questions?

Here are 5 related questions to expand on this topic:
1. How do we determine the domain of a function involving square roots?
2. Why is the expression under the square root required to be non-negative?
3. How do you solve inequalities involving squares like \( x^2 \geq 9 \)?
4. What happens to the domain of the function if the square root were replaced by a different function, like \( f(x) = x^2 - 9 \)?
5. How does the range of this function relate to its domain?

**Tip:** When solving inequalities with squares, always check both positive and negative solutions.

Diketahui fungsi f(x) = √(x² - 9). Daerah asal fungsi f(x) adalah ........

Learn how to find the domain of the function f(x) = √(x² - 9). This algebra problem covers the properties of square roots and how to solve inequalities. Suitable for students in Grades 10-12.

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