Jee Main 2024 31 01 2024 Shift1 - Question8
Question 8
If $f(x)=\frac{4 x+3}{6 x-4}$ and $g(x)=f(f(x))$,
then $g(g(g(g(x))))=$ ?
(1) $x$
(2) $2 x$
(3) $-x$
(4) $-2 x$
Show Answer
Answer: (1)
Solution:
$f(x)=\frac{4 x+3}{6 x-4}$
$g(x)=f(f(x))$
$=\frac{4\left(\frac{4 x+3}{6 x-4}\right)+3}{6\left(\frac{4 x+3}{6 x-4}\right)-4}=\frac{16 x+12+18 x-12}{24 x+18-24 x+16}$
$=\frac{34 x}{34}=x$
$g(g(g(g(x))))=x$
BETA
