JEE Math Practice Question

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

1. A.$$\log _e\left(\frac{4}{9}\right)-1$$
2. B.$$\frac{1}{3} \log _e\left(\frac{4}{9 e^{1 / 3}}\right)$$
3. C.$$\log _e\left(\frac{4}{9 e^{1 / 3}}\right)$$
4. D.$$\frac{1}{3} \log _e\left(\frac{4}{9}\right)+1$$