## Problem of the week

### 2015-23 Fixed points

Let $$f:[0,1)\to[0,1)$$  be a function such that $f(x)=\begin{cases} 2x,&\text{if }0\le 2x\lt 1,\\ 2x-1, & \text{if } 1\le 2x\lt 2.\end{cases}$ Find all $$x$$ such that $f(f(f(f(f(f(f(x)))))))=x.$