1. **State the problem:** Find the domain of the function $$K(x) = \frac{9 - 8x}{x^2 - 8x - 9}$$. 2. **Recall the domain rule:** The domain of a rational function is all real numbers except where the denominator is zero because division by zero is undefined. 3. **Set the denominator equal to zero to find restrictions:** $$x^2 - 8x - 9 = 0$$ 4. **Factor the quadratic:** $$x^2 - 8x - 9 = (x - 9)(x + 1)$$ 5. **Find the roots:** $$x - 9 = 0 \Rightarrow x = 9$$ $$x + 1 = 0 \Rightarrow x = -1$$ 6. **Exclude these values from the domain:** The function is undefined at $$x = 9$$ and $$x = -1$$. 7. **Write the domain in interval notation:** $$(-\infty, -1) \cup (-1, 9) \cup (9, \infty)$$ **Final answer:** The domain of $$K(x)$$ is $$(-\infty, -1) \cup (-1, 9) \cup (9, \infty)$$.