Find the domain of the following functions:
`(1)/(sqrt(25-x^(2)))`

Answer

To find the domain of the function \( f(x) = \frac{1}{\sqrt{25 - x^2}} \), we need to determine the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Identify the function**:
The function is given as \( f(x) = \frac{1}{\sqrt{25 - x^2}} \).

2. **Determine conditions for the square root**:
The expression inside the square root, \( 25 - x^2 \), must be greater than zero for the square root to be defined and for the denominator to be non-zero. Therefore, we set up the inequality:
\[ 25 - x^2 > 0 \]

3. **Rearranging the inequality**:
Rearranging gives:
\[ x^2 < 25 \]

4. **Taking square roots**:
Taking the square root of both sides, we find:
\[ -5 < x < 5 \]
This means \( x \) must be between -5 and 5, but not equal to -5 or 5 since the square root cannot be zero.

5. **Expressing the domain**:
The domain of the function can be expressed in interval notation as:
\[ (-5, 5) \]

### Final Answer:
The domain of the function \( f(x) = \frac{1}{\sqrt{25 - x^2}} \) is \( (-5, 5) \).