JEE Math Practice Question

Let $$\mathrm{g}(x)=f(x)+f(1-x)$$ and $$f^{\prime \prime}(x) > 0, x \in(0,1)$$. If $$\mathrm{g}$$ is decreasing in the interval $$(0, a)$$ and increasing in the interval $$(\alpha, 1)$$, then $$\tan ^{-1}(2 \alpha)+\tan ^{-1}\left(\frac{1}{\alpha}\right)+\tan ^{-1}\left(\frac{\alpha+1}{\alpha}\right)$$ is equal to :

1. A.$$\frac{3 \pi}{4}$$
2. B.$$\pi$$
3. C.$$\frac{5 \pi}{4}$$
4. D.$$\frac{3 \pi}{2}$$