Let $f ( x ) = \frac { 1 - x ( 1 + | 1 - x | ) } { | 1 - x | } \cos \left( \frac { 1 } { 1 - x } \right)$ for $x \neq 1$. Then
[A] $\lim _ { x \rightarrow 1 ^ { - } } f ( x ) = 0$
[B] $\lim _ { x \rightarrow 1 ^ { - } } f ( x )$ does not exist
[C] $\lim _ { x \rightarrow 1 ^ { + } } f ( x ) = 0$
[D] $\lim _ { x \rightarrow 1 ^ { + } } f ( x )$ does not exist