Sets, Relations & Functions
Composite Function — Finding f(g(2))
nta_pyq_2026_jan
Grade 11
Question:
If $g(x)=3x^2+2x-3$, $f(0)=-3$ and $4g(f(x))=3x^2-32x+72$, then $f(g(2))$ is equal to:
$-\dfrac{7}{2}$
$-\dfrac{25}{6}$
$\dfrac{7}{2}$
$\dfrac{25}{6}$
Step-by-Step Solution
Key Concept: Let $f(x)=ax+b$. Then $4g(ax+b)=4(3(ax+b)^2+2(ax+b)-3)=12a^2x^2+(24a^2b+8a)x+(12b^2+8b-12)$. Compare with $3x^2-32x+72$.
$f(x)=\tfrac{x}{2}-3$, $g(2)=13$. $f(g(2))=\tfrac{7}{2}$.
Correct Answer: 3