Sets, Relations & Functions
General
Grade 11
Question:
<p>Let <span class="math-inline">\(f:\{1,2,3,4,5\}\to\{1,2,3,4,5\}\)</span> be one-one with <span class="math-inline">\(f(x)=x+1\iff x\)</span> is even. <span class="math-inline">\(f^{-1}(2)\)</span> can be:</p>
A,B
<strong>B,C</strong>
A,C
A,D
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>Forced: f(2)=3, f(4)=5. Remaining: {1,3,5}→{1,2,4} with f(1)≠2, f(3)≠4.</p><p>f⁻¹(2)=3: possible via f(1)=4,f(3)=2,f(5)=1 ✓</p><p>f⁻¹(2)=5: possible via f(1)=4,f(3)=1,f(5)=2 ✓</p><p>f⁻¹(2)=1: impossible (f(1)≠2)</p><p><strong>Answer: (B),(C)</strong></p><div class="trap-box"><strong>Trap:</strong> The biconditional restricts both even AND odd inputs.</div><div class="key-concept"><strong>Key Concept:</strong> Finite bijection — lock forced values, distribute remainder under constraints</div></div>
Correct Answer: B,C