Let $f : ( - 1 , \infty ) \rightarrow R$ be defined by $f ( 0 ) = 1$ and $f ( x ) = \frac { 1 } { x } \log _ { e } ( 1 + x ) , x \neq 0$. Then the function $f$
(1) Decreases in $( - 1,0 )$ and increases in $( 0 , \infty )$
(2) Increases in $( - 1 , \infty )$
(3) Increases in $( - 1,0 )$ and decreases in $( 0 , \infty )$
(4) Decreases in $( - 1 , \infty )$

In the open interval $(1, e)$, I. The function $\sin ( \ln ( x ) )$ is increasing. II. The function $\cos ( \ln ( x ) )$ is increasing. III. The function $\tan ( \ln ( \mathrm { x } ) )$ is increasing. Which of these statements are true?
A) Only I
B) Only II
C) I and III
D) II and III
E) I, II and III