Let $$f : (1, \infty) \to \mathbf{R}$$ be a function defined as $$f(x) = \frac{x-1}{x+1}$$. Let $$f^{i+1}(x) = f(f^i(x))$$, $$i = 1, 2, ..., 25$$, where $$f^1(x) = f(x)$$. If $$g(x) + f^{26}(x) = 0$$, $$x \in (1, \infty)$$, then the area of the region bounded by the curves $$y = g(x)$$, $$2y = 2x - 3$$, $$y = 0$$ and $$x = 4$$ is :

A

$$\frac{1}{8} + \log_e 2$$

B

$$\frac{1}{4} + \log_e 2$$

C

$$\frac{5}{6} + 3\log_e 2$$

D

$$\frac{5}{6} + \log_e 2$$