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

Options

A. `{-3lexle3}`
B. `{xle-3andxge3}`
C. `{xge3}`
D. `{-3lex}`

Answer

To find the domain of the function \( f(x) = \sqrt{9 - x^2} \), we need to determine the values of \( x \) for which the function is defined. The square root function is defined only when the expression inside the square root is non-negative. Therefore, we need to solve the inequality:

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

2. **Rearrange the inequality**:
\[ 9 \geq x^2 \]
or equivalently,
\[ x^2 \leq 9 \]

3. **Take the square root of both sides**:
To solve \( x^2 \leq 9 \), we take the square root of both sides, remembering that this gives us two cases (positive and negative):
\[ -3 \leq x \leq 3 \]

4. **Write the domain in interval notation**:
The values of \( x \) that satisfy this inequality are from -3 to 3, inclusive. Therefore, the domain of the function can be expressed in interval notation as:
\[ [-3, 3] \]

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