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