Question:

<div class="solution"><p><strong>Step 1:</strong> Domain = intersection of domains of all three terms.</p><p>• <span class="math-inline">$\sin^{-1}x$</span>: <span class="math-inline">$[-1,1]$</span><br>• <span class="math-inline">$\tan^{-1}x$</span>: <span class="math-inline">$\mathbb{R}$</span><br>• <span class="math-inline">$\sec^{-1}x$</span>: <span class="math-inline">$(-\infty,-1]\cup[1,\infty)$</span></p><p>Intersection: <span class="math-inline">$\{-1,1\}$</span> only.</p><p><strong>Step 2:</strong> <span class="math-block">$$f(1)=\frac{\pi}{2}+\frac{\pi}{4}+0=\frac{3\pi}{4}$$</span><span class="math-block">$$f(-1)=-\frac{\pi}{2}-\frac{\pi}{4}+\pi=\frac{\pi}{4}$$</span></p><p><strong>Answer: (C) <span class="math-inline">$\{\pi/4,\,3\pi/4\}$</span></strong> (two discrete values)</p><div class="trap-box"><strong>Trap:</strong> Assuming the range is a continuous interval. The domain is only two points.</div><div class="key-concept"><strong>Key Concept:</strong> Identify domain first — a discrete domain gives a discrete range</div></div>