Sets, Relations & Functions
General
Grade 11
Question:
<p>Piecewise <span class="math-inline">\(f\)</span>: <span class="math-inline">\(x^2\)</span> on <span class="math-inline">\((0,2)\)</span>, <span class="math-inline">\(2x-3\)</span> on <span class="math-inline">\([2,3)\)</span>, <span class="math-inline">\(x+2\)</span> on <span class="math-inline">\([3,\infty)\)</span>. Which are correct?</p>
A,B,C,D
<strong>A,B,C</strong>
A,C
B,C,D
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>(A) f(3/2)=9/4; f(9/4)=9/2-3=3/2; f(3/2)=9/4 ✓</p><p>(B) f(5/2)=2; f(2)=1; f(1)=1; so 1+1=2=f(5/2) ✓</p><p>(C) f(1)=1; f(f(1))=f(1)=1 ✓; (D) false.</p><p><strong>Answer: (A),(B),(C)</strong></p><div class="trap-box"><strong>Trap:</strong> Output of one branch can fall into a different branch on next iteration. Re-check interval each time.</div><div class="key-concept"><strong>Key Concept:</strong> Piecewise iteration — branch-tracing, slow and exact</div></div>
Correct Answer: A,B,C