A function $f$ defined on the set of real numbers satisfies the inequalities
$$1 \leq f ( x ) \leq 2$$
for every $x$.
Accordingly,\
I. $\lim _ { x \rightarrow 1 } \frac { 1 } { f ( x ) }$ exists.\
II. $\lim _ { x \rightarrow 1 } \frac { f ( x ) } { x }$ exists.\
III. $\lim _ { x \rightarrow 1 } ( | f ( x ) | - f ( x ) )$ exists.
Which of the following statements are always true?\
A) Only I\
B) Only II\
C) Only III\
D) I and II\
E) II and III