\displaystyle f(x)=\begin{cases}  1.5 x &\mbox{if } x\in(0,\frac{1}{2}), \\  2^{n+1}\cdot\left(x-\left(1-\frac{1}{2^{n}}\right)\right) &\mbox{if } x\in\left(1-\frac{1}{2^{n}},1-\frac{1}{2^{n+1}}\right) \text{ for all } n\geq 1.\end{cases}