Let f: A \to B be an onto function such that f(x) = \sqrt{-x - 2 - 2\sqrt{-3 - \sqrt{-x - 2 + 2\sqrt{-x - 3}}}, then set 'B' is-
Step-by-Step Solution
<div class="solution"><p>Let u=log₂x≥0. Then y=(u+1)²+2, so u+1=√(y-2) (positive branch). Thus x=2^{-1+√(y-2)}.</p><p>Range of f is [3,∞) → domain of f⁻¹ is [3,∞).</p><p><strong>Answer: (A),(D)</strong></p><div class="trap-box"><strong>Trap:</strong> Negative root is invalid since log₂x≥0 on given domain.</div><div class="key-concept"><strong>Key Concept:</strong> Log-inside-quadratic → substitute u=logₐx first</div></div>
Correct Answer: A