Write the domain of the following real functions
`sqrt(9-x^(2))`

Answer

To find the domain of the function \( f(x) = \sqrt{9 - x^2} \), we need to ensure that the expression under the square root is non-negative. This means we need to solve the inequality:

1. **Set up the inequality**:
\[ 9 - x^2 \geq 0 \]

2. **Rearrange the inequality**:
\[ -x^2 \geq -9 \]
Multiplying both sides by -1 (and reversing the inequality) gives:
\[ x^2 \leq 9 \]

3. **Take the square root**:
To solve \( x^2 \leq 9 \), we take the square root of both sides:
\[ -3 \leq x \leq 3 \]

4. **Write the domain in interval notation**:
The domain of the function \( f(x) \) is:
\[ x \in [-3, 3] \]

Thus, the domain of the function \( f(x) = \sqrt{9 - x^2} \) is \( [-3, 3] \).