The domain of the function f defined by `f(x)= sqrt(x^(2)-9)` is

Options

A. `[-3,3]`
B. `(-3,3)`
C. `(-oo,-3]uu[3,oo)`
D. [0,3]

Answer

To find the domain of the function \( f(x) = \sqrt{x^2 - 9} \), we need to determine the values of \( x \) for which the expression under the square root is non-negative (i.e., greater than or equal to zero).

### Step-by-Step Solution:

1. **Set the expression under the square root greater than or equal to zero:**
\[ x^2 - 9 \geq 0 \]

2. **Rearranging the inequality:**
\[ x^2 \geq 9 \]

3. **Taking the square root of both sides:**
Since we are dealing with a square, we need to consider both the positive and negative roots:
\[ |x| \geq 3 \]
This implies:
\[ x \geq 3 \quad \text{or} \quad x \leq -3 \]

4. **Expressing the solution in interval notation:**
The solution can be expressed as:
\[ (-\infty, -3] \cup [3, \infty) \]

5. **Conclusion:**
Therefore, the domain of the function \( f(x) = \sqrt{x^2 - 9} \) is:
\[ \text{Domain} = (-\infty, -3] \cup [3, \infty) \]