Let the function $f ( x ) = \ln | 2 x + 1 | - \ln | 2 x - 1 |$ . Then $f ( x )$ A． is an even function and monotonically increasing on $\left( \frac { 1 } { 2 } , + \infty \right)$ B． is an odd function and monotonically decreasing on $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ C． is an even function and monotonically increasing on $\left( - \infty , - \frac { 1 } { 2 } \right)$ D． is an odd function and monotonically decreasing on $\left( - \infty , - \frac { 1 } { 2 } \right)$
Let the function $f ( x ) = \ln | 2 x + 1 | - \ln | 2 x - 1 |$ . Then $f ( x )$
A． is an even function and monotonically increasing on $\left( \frac { 1 } { 2 } , + \infty \right)$
B． is an odd function and monotonically decreasing on $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$
C． is an even function and monotonically increasing on $\left( - \infty , - \frac { 1 } { 2 } \right)$
D． is an odd function and monotonically decreasing on $\left( - \infty , - \frac { 1 } { 2 } \right)$