Let $$f:R \rightarrow R$$ and $$g:R\rightarrow R$$ be two non-constant differentiable functions. If $$f'(x) = (e^{(f(x)-g(x))}) g'(x)$$ for all $$x \in R$$, and $$f(1) = g(2) = 1$$, then which of the following statement(s) is (are) TRUE?

A

$$f(2)<1-log_{e} {2}$$

B

$$f(2)>1-log_{e} {2}$$

C

$$g(1)<1-log_{e} {2}$$

D

$$g(1)>1-log_{e} {2}$$