The random variable X has mass function
$p(x) = \begin{cases} \frac{1}{2} \text{ } x=1 \\ \frac{1}{3} \text{ } x = 2 \\ \frac{1}{6} \text{ } x = 3. \end{cases}$
Find $E(g(X))$ where $g(x) = x^2 + x + 1$.

Please answer to 3 decimal places.