Sets, Relations & Functions
General
Grade 11
Question:
<p>If <span class="math-inline">\(g(x)=x^2+x-1\)</span> and <span class="math-inline">\((g\circ f)(x)=4x^2-10x+5\)</span>, find <span class="math-inline">\(f\!\left(\frac{5}{4}\right)\)</span>.</p>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>Observe g(2x-3)=4x²-10x+5. So f(x)=2x-3 or 2-2x. At x=5/4: both give -1/2. Answer: -1/2.</p><div class="trap-box"><strong>Trap:</strong> Even if g not one-one, the asked value can still be unique at a specific point.</div><div class="key-concept"><strong>Key Concept:</strong> Reverse-engineer g rather than solving quadratic in f(x)</div></div>
Correct Answer: -1/2