Let the function $\mathrm{g}:(-\infty, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ be given by $\mathrm{g}(\mathrm{u})=2 \tan ^{-1}\left(\mathrm{e}^{\mathrm{u}}\right)-\frac{\pi}{2}$. Then, g is
Select the correct option:
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 $(-\infty, \infty)$
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