Find the range of the function $f(x) = \sin^{-1} x + \cos^{-1} x + \tan^{-1} x$.
Step-by-Step Solution
Domain $= [-1, 1] \Rightarrow \sin^{-1}x + \cos^{-1}x = \pi/2$. [1.0 Mark]
\tan^{-1} x \in [-\pi/4, \pi/4]$ for $x \in [-1, 1]$. [1.0 Mark]
Range $= [\pi/4, 3\pi/4]$. [1.0 Mark]
---
🎯 Official CBSE Marking Scheme:
Identifying domain $[-1, 1]$ and applying constant sum identity: 1.0 Mark
Evaluating bounds for $\tan^{-1} x$: 1.0 Mark
Evaluating range $[\pi/4, 3\pi/4]$: 1.0 Mark
Correct Answer: