Domain of `sqrt(a^(2)-x^(2))(agt0)` is (i) [-a,a]`(ii)` (-a,a)` (iii) ` [0,a]` (iv) ` [-a,0]`

Options

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

Explanation

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 expression under the square root is non-negative.

### Step-by-Step Solution:

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

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

3. **Take the square root of both sides:**
Since \( a > 0 \), we can take the square root without changing the inequality:
\[ \sqrt{a^2} \geq \sqrt{x^2} \]
This simplifies to:
\[ a \geq |x| \]

4. **Interpret the absolute value inequality:**
The inequality \( a \geq |x| \) means that \( x \) must lie within the range defined by:
\[ -a \leq x \leq a \]

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

### Conclusion:
The correct option for the domain of \( f(x) = \sqrt{a^2 - x^2} \) is (i) \([-a, a]\).