1. **State the problem:** Determine the domain of the function $$f(z) = \frac{z}{z-4}$$. 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 and solve:** $$z - 4 = 0$$ $$z = 4$$ 4. **Exclude this value from the domain:** The function is undefined at $$z = 4$$. 5. **Write the domain:** All real numbers except $$4$$. **Final answer:** $$\text{Domain} = \{ z \in \mathbb{R} \mid z \neq 4 \}$$