Sets, Relations & Functions
General
Grade 11
Question:
<p>Piecewise functions <span class="math-inline">\(f\)</span> and <span class="math-inline">\(g\)</span> given. Which are true?<br>(A) <span class="math-inline">\((f+g)(1)=9\)</span> (B) <span class="math-inline">\((f-g)(3.5)=1\)</span> (C) <span class="math-inline">\((fg)(0)=24\)</span> (D) <span class="math-inline">\((f/g)(5)=8/3\)</span></p>
A,B,C,D
<strong>A,B,C</strong>
B,C,D
A,C,D
Step-by-Step Solution
Key Concept: General
<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: A,B,C