<p>Range of \(f(x)=\sin^{-1}x+\cos^{-1}x+\tan^{-1}x\) is:</p>
Step-by-Step Solution
<div class="solution"><p>Use $\sin^{-1}x+\cos^{-1}x=\pi/2$ (constant on domain [-1,1]). Then $f(x)=\pi/2+\tan^{-1}x$. Range of $\tan^{-1}x$ on [-1,1] is $[-\pi/4,\pi/4]$. So range = $[\pi/4,3\pi/4]$.</p><div class="key-concept"><strong>Key Concept:</strong> Collapse sin⁻^1+cos⁻^1=\pi/2 immediately
Correct Answer: [π/4, 3π/4]