Sets, Relations & Functions
Grade 11
Question:
<p>Piecewise \(f\): \(x^2\) on \((0,2)\), \(2x-3\) on \([2,3)\), \(x+2\) on \([3,\infty)\). Which are correct?</p>
A,B,C,D
<strong>A,B,C</strong>
A,C
B,C,D
Step-by-Step Solution
<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 class="key-concept"><strong>Key Concept:</strong> Piecewise iteration -- branch-tracing, slow and exact
Correct Answer: A,B,C