Range of f(x) = sin^−1x + tan^−1x + cos^−1x is

$x ∈ [−1, 1]⇒\sin^{−1}x + \cos^{−1}x=\frac{π}{2}$

so $f(x)=\frac{π}{2}+\tan^{-1}x$

$\tan^{-1}x∈\left[-\frac{π}{4},\frac{π}{4}\right]$

$⇒\frac{π}{2}+\tan^{-1}x∈\left[\frac{π}{4},\frac{3π}{4}\right]$