Let D be the domain of the real valued function `f` defined by ` f(x)=sqrt(25-x^(2))` . Then, write D.

Explanation

To find the domain \( D \) of the function \( f(x) = \sqrt{25 - x^2} \), we need to ensure that the expression inside the square root is non-negative. This is because the square root of a negative number is not defined in the set of real numbers.

### Step-by-Step Solution:

1. **Set the expression inside the square root greater than or equal to zero:**
\[ 25 - x^2 \geq 0 \]

2. **Rearrange the inequality:**
\[ -x^2 \geq -25 \]
By multiplying both sides by -1 (which reverses the inequality), we get:
\[ x^2 \leq 25 \]

3. **Take the square root of both sides:**
\[ |x| \leq 5 \]
This means that \( x \) can take values from -5 to 5.

4. **Express the result in interval notation:**
\[ -5 \leq x \leq 5 \]
Thus, the domain \( D \) can be written as:
\[ D = [-5, 5] \]

### Final Answer:
The domain \( D \) of the function \( f(x) = \sqrt{25 - x^2} \) is:
\[ D = [-5, 5] \]