Find the domain of the function \(f(x) = \frac{1}{x^2 - 4}\).

Step 1 ：The domain of a function is the set of all real numbers for which the function is defined. In the case of a rational function, the function is undefined where the denominator is equal to zero.

Step 2 ：To find the values of \(x\) that make the denominator zero, we set \(x^2 - 4 = 0\) and solve for \(x\).

Step 3 ：\(x^2 - 4 = 0\) is a quadratic equation, and can be factored into \((x - 2)(x + 2) = 0\).

Step 4 ：Setting each factor equal to zero gives us \(x - 2 = 0\) and \(x + 2 = 0\), so \(x = 2\) and \(x = -2\) are the values that make the denominator zero.

Step 5 ：Therefore, the function is undefined at \(x = 2\) and \(x = -2\).

Step 6 ：The domain of the function is the set of all real numbers except \(x = 2\) and \(x = -2\). This can be written in interval notation as \((-\infty, -2) \cup (-2, 2) \cup (2, \infty)\).