Consider the following three statements for the function $$f: (0, \infty ) \rightarrow \mathbb R$$ defined by
$$f(x)= |\log_{e}{x}|-|x-1|:$$
(I)f is differentiable at all x > 0.
(II)f is increasing in (0, 1).
(III)f is decreasing in (1, $$\infty$$).
Then.

A

Only (I) and (III) are TRUE.

B

Only (II) and (III) are TRUE.

C

All (I), (II) and (III) are TRUE.

D

Only (I) is TRUE.