Question

Let f^1(x)=\frac{3 x+2}{2 x+3}, x \in R -\left\\{\frac{-3}{2}\right\\} For $n \geq 2$, define $f^{ n }(x)=f^1 o f^{ n -1}(x)$ if $f^5(x)=\frac{ a x+ b }{ b x+ a }, \operatorname{gcd}( a , b )=1$, then $a + b$ is equal to ______.

Answer 1

The correct answer is 3125.
f1(x)=2x+33x+2​
⇒f2(x)=12x+1313x+12​
⇒f3(x)=62x+6363x+62​
∴f5(x)=1562x+15631563x+1562​
a+b=3125