Sets, Relations & Functions
Composition of Functions — g(g(g(x)))
nta_pyq_2024_jan
Grade 11
Question:
If $f(x)=\dfrac{4x+3}{6x-4}$, $x\neq\dfrac{2}{3}$ and $(f\circ f)(x)=g(x)$, where $g:\mathbb{R}-\left\{\dfrac{2}{3}\right\}\to\mathbb{R}-\left\{\dfrac{2}{3}\right\}$, then $(g\circ g\circ g)(4)$ is equal to
$-\dfrac{19}{20}$
$\dfrac{19}{20}$
$-4$
$4$
Step-by-Step Solution
Key Concept: Compute $f(f(x))$ — show it simplifies to $g(x)=x$. Then $g(g(g(4)))=4$.
$f(f(x))=x$, so $g(x)=x$. $g(g(g(4)))=4$.
Correct Answer: 4