The domain of the functionf detined by `f(x)= sqrt(a^(2)-x^(2)),(agt 0)` is

Options

A. (-a,a)
B. [-a,a]
C. [0,a]
D. (-a,0]

Answer

To find the domain of the function \( f(x) = \sqrt{a^2 - x^2} \) where \( a > 0 \), we need to determine the values of \( x \) for which the function is defined. The function is defined when the expression inside the square root is non-negative.

### Step-by-step solution:

1. **Identify the condition for the square root**:
The expression inside the square root must be greater than or equal to zero:
\[ a^2 - x^2 \geq 0 \]

2. **Rearrange the inequality**:
Rearranging gives:
\[ a^2 \geq x^2 \]

3. **Take square roots**:
Taking the square root of both sides (keeping in mind that \( a > 0 \)):
\[ |x| \leq a \]
This implies:
\[ -a \leq x \leq a \]

4. **Express the domain**:
The values of \( x \) that satisfy this inequality form the interval:
\[ [-a, a] \]
Since both endpoints are included (as the inequality is non-strict), this is a closed interval.

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