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