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

• A
  even and is strictly increasing in $(0, \infty)$
• B
  odd and is strictly decreasing in $(-\infty, \infty)$
• ✓
  odd and is strictly increasing in $(-\infty, \infty)$
• D
  neither even nor odd, but is strictly increasing in $(-\infty, \infty)$