Let f^1(x)=(3 x+2)/(2 x+3), x ∈ R -{-3/2} For n ≥ 2, define f^n (x)=f^1 ° f^n -1 (x). If f^5(x)=(a x+ b)/(b x+ a), gcd ( a, b )=1, then a + b is…

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