Let the function $g : ( - \infty , \infty ) \rightarrow \left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ be given by $g ( u ) = 2 \tan ^ { - 1 } \left( e ^ { u } \right) - \frac { \pi } { 2 }$. Then, $g$ is\\
(A) even and is strictly increasing in $(0 , \infty)$\\
(B) odd and is strictly decreasing in $( - \infty , \infty )$\\
(C) odd and is strictly increasing in $( - \infty , \infty )$\\
(D) neither even nor odd, but is strictly increasing in $( - \infty , \infty )$