1. **State the problem:** Find the domain of the function $$f(x) = \frac{x - 9}{x + 1}$$. 2. **Recall the domain rule:** The domain of a function includes all real numbers except where the denominator is zero because division by zero is undefined. 3. **Set the denominator equal to zero and solve:** $$x + 1 = 0$$ $$x = -1$$ 4. **Exclude this value from the domain:** The function is undefined at $$x = -1$$. 5. **Write the domain:** All real numbers except $$x = -1$$, which in interval notation is: $$(-\infty, -1) \cup (-1, \infty)$$. **Final answer:** The domain of $$f(x)$$ is all real numbers except $$x = -1$$.