1. **State the problem:** We are given two functions: $$g(x) = -2x^4 + 4$$ $$h(x) = -3x^3 - 5$$ and a value $$x = 3$$. We need to find: a) $$(g + h)(3)$$ b) $$(g - h)(3)$$ c) $$(g \cdot h)(3)$$ 2. **Recall the formulas:** - Sum of functions: $$(g + h)(x) = g(x) + h(x)$$ - Difference of functions: $$(g - h)(x) = g(x) - h(x)$$ - Product of functions: $$(g \cdot h)(x) = g(x) \times h(x)$$ 3. **Calculate each function at $$x=3$$:** - Calculate $$g(3)$$: $$g(3) = -2(3)^4 + 4 = -2(81) + 4 = -162 + 4 = -158$$ - Calculate $$h(3)$$: $$h(3) = -3(3)^3 - 5 = -3(27) - 5 = -81 - 5 = -86$$ 4. **Calculate each expression:** a) $$(g + h)(3) = g(3) + h(3) = -158 + (-86) = -244$$ b) $$(g - h)(3) = g(3) - h(3) = -158 - (-86) = -158 + 86 = -72$$ c) $$(g \cdot h)(3) = g(3) \times h(3) = (-158) \times (-86) = 13588$$ **Final answers:** a) $-244$ b) $-72$ c) $13588$