Let r be a real number and f(x)={2x−ramp;ifx≥rramp;ifxlt;rf(x) = \begin{cases}2x -r & ifx \geq r\\ r &ifx < r\end{cases}f(x)={2x−rramp;ifx≥ramp;ifxlt;r. Then, the equation f(x)=f(f(x))f(x) = f(f(x))f(x)=f(f(x)) holds for all real values of xxx where
x > r
x≤rx \leq rx≤r
x≠rx \neq rx=r
x≥rx \geq rx≥r
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