1. **State the problem:** We are given the function $g(x) = 1 + \left(\frac{2x^{3}}{2} - x^{2}\right)$ and need to simplify it. 2. **Write the function clearly:** $$g(x) = 1 + \left(\frac{2x^{3}}{2} - x^{2}\right)$$ 3. **Simplify the fraction:** $$\frac{2x^{3}}{2} = \cancel{\frac{2}{2}} x^{3} = x^{3}$$ 4. **Rewrite the function with the simplified term:** $$g(x) = 1 + (x^{3} - x^{2})$$ 5. **Remove parentheses:** $$g(x) = 1 + x^{3} - x^{2}$$ 6. **Final simplified form:** $$g(x) = x^{3} - x^{2} + 1$$ This is the simplified expression for the given function.