Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that $f^{\prime \prime}(\mathrm{x})>0$ for all $\mathrm{x} \in \mathbf{R}$ and $f^{\prime}(\mathrm{a}-1)=0$, where a is real number. Let $\mathrm{g}(\mathrm{x})=f\left(\tan ^{2} \mathrm{x}-2 \tan \mathrm{x}+\mathrm{a}\right)$, $0<\mathrm{x}<\frac{\pi}{2}.\\$ Consider the following two statements :$\\$(I) g is increasing in $\left(0, \frac{\pi}{4}\right)\\$ (II) g is decreasing in $\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$