Sets, Relations & Functions
General
Grade 11
Question:
<p>For suitable \(a\), \(f(x)=\dfrac{a-x}{a+x}\) with \((f\circ f)(x)=x\). Find \(f\!\left(-\frac{1}{2}\right)\).</p>
Step-by-Step Solution
<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
Correct Answer: 3