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 \[ f(f(f(f(f(f(f(x)))))))=x.\]

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2015-23 Fixed points, 1.9 out of 5 based on 7 ratings