1. **State the problem:** We are given the function $$g(x) = 1 - 2(x+2)^2 - \ln(x+2)$$ and we want to understand or analyze it. 2. **Rewrite the function clearly:** $$g(x) = 1 - 2(x+2)^2 - \ln(x+2)$$ 3. **Important domain note:** The natural logarithm function $$\ln(x+2)$$ is defined only for $$x+2 > 0$$, so the domain of $$g(x)$$ is $$x > -2$$. 4. **Explain components:** - The term $$-2(x+2)^2$$ is a quadratic expression scaled by -2, which opens downward. - The term $$-\ln(x+2)$$ decreases as $$x+2$$ increases because of the negative sign. 5. **No further simplification is possible without specific tasks (like finding roots, derivatives, etc.).** Final function: $$g(x) = 1 - 2(x+2)^2 - \ln(x+2)$$ This is the explicit form of the function with domain $$x > -2$$.