Question 25
Let $f(x)=\frac{x+6}{x}$ and $f_n(x)=f(f(\cdots f(f(x))\cdots))$ be the $n$-fold composite of $f$. For example, $f_2(x)=\frac{\frac{x+6}{x}+6}{\frac{x+6}{x}}=\frac{7x+6}{x+6}$ and $f_3(x)=\frac{\frac{7x+6}{x+6}+6}{\frac{7x+6}{x+6}}=\frac{13x+42}{7x+6}$.
Let $S$ be the complete set of real solutions of the equation $f_n(x)=x$. The number of elements in $S$ is
Let $S$ be the complete set of real solutions of the equation $f_n(x)=x$. The number of elements in $S$ is