Let $$f : R \to R$$ and $$g : R \to R$$ be two functions defined by $$f(x) = \log_e(x^2 + 1) - e^{-x} + 1$$ and $$g(x) = \frac{1 - 2e^{2x}}{e^x}$$. Then, for which of the following range of $$\alpha$$, the inequality $$f\left(g\left(\frac{\alpha - 1}{3}\right)\right) > f\left(g\left(\alpha - \frac{5}{3}\right)\right)$$ holds?

A

$$(-2, -1)$$

B

$$(2, 3)$$

C

$$(1, 2)$$

D

$$(-1, 1)$$