Sets, Relations & Functions
General
Grade 11
Question:
<p>Additive \(f\) with \(f(-3/5)=12\); multiplicative positive \(g\) with \(g(-1/3)=2\). Find \(\{f(1/4)+g(-2)-8\}g(0)\).</p>
Step-by-Step Solution
<div class="solution"><p>f(-3/5)=(-3/5)f(1)=12 \to f(1)=-20 \to f(1/4)=-5.</p><p>g(x)=aˣ, a^{-1/3}=2 \to a=1/8. g(-2)=(1/8)^{-2}=64. g(0)=1.</p><p>{-5+64-8}·1=51.</p><p><strong>Answer: 51</strong></p><div class="trap-box"><strong>Trap:</strong> g(0)=1 follows from g(0)=g(0+0)=g(0)^2.<div class="key-concept"><strong>Key Concept:</strong> Additive \to linear; positive multiplicative \to exponential
Correct Answer: 51