Composition Equation for f(x)

Let r be a real number and f(x) = $\left\{\begin{array}{cc}2\mathrm{x}-\mathrm{r}& \mathrm{if} \mathrm{x}\ge \mathrm{r}\\ \mathrm{r}& \mathrm{if} \mathrm{x}<\mathrm{r}\end{array}.\right.$Then, the equation f(x) = f(f(x)) holds for all real values of x where