Maclaurin Series Coefficient for a Composite Function

The function $f$ is represented by its Maclaurin series, $f(x) = 2x + x^2 + \displaystyle\frac{1}{3}x^3 + \displaystyle\frac{1}{12}x^4 + \cdots$, which converges for all real numbers $x$. If a function $g$ is defined by $g(x) = \displaystyle\frac{1}{1 + f(x)}$, what is the coefficient of $x^3$ in the Maclaurin series for $g$?