Find the domain of the following functions:
`(1)/(x^(2)-4)`

Answer

To find the domain of the function \( f(x) = \frac{1}{x^2 - 4} \), we need to determine the values of \( x \) for which the function is defined. The function is undefined when the denominator is equal to zero.

### Step-by-Step Solution:

1. **Identify the Denominator**:
The function is given by \( f(x) = \frac{1}{x^2 - 4} \). Here, the denominator is \( x^2 - 4 \).

2. **Set the Denominator to Zero**:
To find where the function is undefined, we set the denominator equal to zero:
\[ x^2 - 4 = 0 \]

3. **Solve for \( x \)**:
Rearranging the equation gives:
\[ x^2 = 4 \]
Taking the square root of both sides, we find:
\[ x = 2 \quad \text{or} \quad x = -2 \]

4. **Determine the Domain**:
The function is undefined at \( x = 2 \) and \( x = -2 \). Therefore, the domain of the function is all real numbers except these two values. In interval notation, this can be expressed as:
\[ \text{Domain} = (-\infty, -2) \cup (-2, 2) \cup (2, \infty) \]

### Final Answer:
The domain of the function \( f(x) = \frac{1}{x^2 - 4} \) is:
\[ \text{Domain} = \{ x \in \mathbb{R} \mid x \neq -2, x \neq 2 \} \]