1. **State the problem:** Find the domain of the function $$f(x) = \frac{2}{x^{2} - 64}$$. 2. **Recall the domain rule for rational functions:** The domain includes all real numbers except where the denominator is zero because division by zero is undefined. 3. **Set the denominator equal to zero to find excluded values:** $$x^{2} - 64 = 0$$ 4. **Solve for $x$:** $$x^{2} = 64$$ $$x = \pm 8$$ 5. **Interpretation:** The function is undefined at $x = 8$ and $x = -8$. 6. **Write the domain:** All real numbers except $x = 8$ and $x = -8$. In interval notation, the domain is: $$(-\infty, -8) \cup (-8, 8) \cup (8, \infty)$$