APFIVE Maclaurin Series Coefficient for a Composite Function
A function $$f$$ has a Maclaurin series given by $$2x + x^2 + \displaystyle\frac{1}{3}x^3 + \displaystyle\frac{1}{12}x^4 + \cdots$$, and the Maclaurin series converges to $$f(x)$$ for all real numbers $$x$$. If $$g$$ is the function defined by $$g(x) = \displaystyle\frac{1}{1 + f(x)}$$, what is the coefficient of $$x^3$$ in the Maclaurin series for $$g$$?
A
$$-\displaystyle\frac{13}{3}$$
B
$$-\displaystyle\frac{14}{3}$$
C
$$-5$$
D
$$-\displaystyle\frac{11}{3}$$
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