functions - Bijection between $[0,1]$ and $[0,1)$

Could one give me a bijection between $[0,1]$ and $[0,1)$ ?

I am trying to find a function $f:[0,2]\to[0,2]$ such that $\forall0\le x\le2,f^{-1}(x)$ is a tuple (2 elements), and such a bijection would give me an answer easily.