Sets, Relations & Functions
General
Grade 11
Question:
<p>Let \(f(x)=\dfrac{x-2}{x-3}\), \(g(x)=2x-3\). Find sum of all \(x\) where \(f^{-1}(x)+g^{-1}(x)=\frac{13}{2}\).</p>
Step-by-Step Solution
<div class="solution"><p>f⁻^1(x)=(3x-2)/(x-1); g⁻^1(x)=(x+3)/2. Sum=(3x-2)/(x-1)+(x+3)/2=13/2. Solving: multiply out, get quadratic with sum of roots=5.</p><div class="key-concept"><strong>Key Concept:</strong> Explicit inverse + Vieta's sum of roots
Correct Answer: 5