- Home
- Standard 12
- Mathematics
1.Relation and Function
hard
Let $f ^1( x )=\frac{3 x +2}{2 x +3}, x \in R -\left\{\frac{-3}{2}\right\}$ For $n \geq 2$, define $f ^{ n }( x )= f ^1 0 f ^{ n -1}( x )$. If $f ^5( x )=\frac{ ax + b }{ bx + a }, \operatorname{gcd}( a , b )=1$, then $a + b$ is equal to $............$.
A
$3124$
B
$3123$
C
$3126$
D
$3125$
(JEE MAIN-2023)
Solution
$f^1(x)=\frac{3 x+2}{2 x+3}$
$\Rightarrow f^2(x)=\frac{13 x+12}{12 x+13}$
$\Rightarrow f^3(x)=\frac{63 x+62}{62 x+63}$
$\therefore f^5(x)=\frac{1563 x+1562}{1562 x+1563}$
$a+b=3125$
Standard 12
Mathematics
