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