<p>Piecewise functions \(f\) and \(g\) given. Which are true?<br>(A) \((f+g)(1)=9\) (B) \((f-g)(3.5)=1\) (C) \((fg)(0)=24\) (D) \((f/g)(5)=8/3\)</p>
Step-by-Step Solution
<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 \to 9 ✓</p><p>(B) f(3.5)=10.5, g(3.5)=9.5 \to 1 ✓</p><p>(C) f(0)=4, g(0)=6 \to 24 ✓</p><p>(D) f(5)=12, g(5)=32 \to 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 class="key-concept"><strong>Key Concept:</strong> Piecewise evaluation -- settle branch before any operation
Correct Answer: A,B,C