Sets, Relations & Functions
General
Grade 11
Question:
<p>For suitable <span class="math-inline">\(a\)</span>, <span class="math-inline">\(f(x)=\dfrac{a-x}{a+x}\)</span> with <span class="math-inline">\((f\circ f)(x)=x\)</span>. Find <span class="math-inline">\(f\!\left(-\frac{1}{2}\right)\)</span>.</p>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>Involution condition forces a=1. f(x)=(1-x)/(1+x). f(-1/2)=(3/2)/(1/2)=3.</p><div class="key-concept"><strong>Key Concept:</strong> Möbius transformation involution — unique parameter value</div></div>
Correct Answer: 3