Question 123
Define a function $f$ on the real numbers by
$$
f(x)= \begin{cases}2 x & \text{ if } x\lt 1 / 2 \\ 2 x-1 & \text{ if } x \geq 1 / 2\end{cases}
$$
Determine all values $x$ satisfying $f(f(f(f(f(x)))))=x$.
$$
f(x)= \begin{cases}2 x & \text{ if } x\lt 1 / 2 \\ 2 x-1 & \text{ if } x \geq 1 / 2\end{cases}
$$
Determine all values $x$ satisfying $f(f(f(f(f(x)))))=x$.