Range of function f(x) = \log_2 \left( \frac{4}{\sqrt{x+2}+\sqrt{2-x}} \right) is given by
Step-by-Step Solution
Key Concept: Evaluate each option using the correct branch first.
<div class="solution"><p><strong>Key Idea:</strong> Evaluate each option using the correct branch first.</p><p>(A) f(1)=2, g(1)=7 → 9 ✓</p><p>(B) f(3.5)=10.5, g(3.5)=9.5 → 1 ✓</p><p>(C) f(0)=4, g(0)=6 → 24 ✓</p><p>(D) f(5)=12, g(5)=32 → 12/32=3/8 ≠ 8/3 ✗</p><p><strong>Answer: (A),(B),(C)</strong></p><div class="trap-box"><strong>Trap:</strong> Applying the wrong branch to x=3.5 or x=5 is the most common error.</div><div class="key-concept"><strong>Key Concept:</strong> Piecewise evaluation — settle branch before any operation</div></div>
Correct Answer: B