\[g(x) = 2x - \frac{1}{3}x^{2};\ \]
\[g\left( \frac{1}{2} \right) = 2 \cdot \frac{1}{2} - \frac{1}{3} \cdot \left( \frac{1}{2} \right)^{2} =\]
\[= 1 - \frac{1}{3} \cdot \frac{1}{4} = 1 - \frac{1}{12} = \frac{11}{12}.\]