Functions Question 12
Question 12 - 2024 (31 Jan Shift 1)
If $f(x)=\frac{4 x+3}{6 x-4}, x \neq \frac{2}{3}$ and $(f \circ f)(x)=g(x)$, where $g: \mathbb{R}-\left{\frac{2}{3}\right} \rightarrow \mathbb{R}-\left{\frac{2}{3}\right}$, then (gogog) (4) is equal to
(1) $-\frac{19}{20}$
(2) $\frac{19}{20}$
(3) -4
(4) 4
Show Answer
Answer (4)
Solution
$f(x)=\frac{4 x+3}{6 x-4}$
$g(x)=\frac{4\left(\frac{4 x+3}{6 x-4}\right)+3}{6\left(\frac{4 x+3}{6 x-4}\right)-4}=\frac{34 x}{34}=x$
$g(x)=x \therefore g(g(g(4)))=4$
