Let $$g(x)$$ be a linear function and $$f(x) = \begin{cases} g(x), & x \leq 0 \\ \left(\frac{1+x}{2+x}\right)^{1/x}, & x > 0 \end{cases}$$, is continuous at $$x = 0$$. If $$f'(1) = f(-1)$$, then the value of $$g(3)$$ is

A

$$\frac{1}{3}\log_e\frac{4}{9e^{1/3}}$$

B

$$\frac{1}{3}\log_e\frac{4}{9} + 1$$

C

$$\log_e\frac{4}{9} - 1$$

D

$$\log_e\frac{4}{9e^{1/3}}$$