Final answer:
The domain of the function f(x) = -x²-9-6x can be found by considering two conditions: 0 < x < 2 and x ≥ 2. The domain is the set of all real numbers greater than or equal to 0, excluding 0, and all real numbers greater than or equal to 2.
Step-by-step explanation:
The domain of the function f(x) = -x²-9-6x can be found by considering the two given conditions:
- If 0 < x < 2, then the function is defined for all values of x between 0 and 2, excluding 0 and 2.
- If x ≥ 2, then the function is defined for all values of x greater than or equal to 2.
Therefore, the domain of the function is the set of all real numbers greater than or equal to 0, excluding 0, and all real numbers greater than or equal to 2.