Could you tell me a function that is bijective?

Could you tell me a function that is bijective? The domain and codomain of the function must be $[0,1)$. I can't find any bijection. Please help me!

Answer

The identity function $\mathrm{id} : [0,1) \to [0,1)$ defined as $\mathrm{id}(x) := x$ for all $x \in [0,1)$ is a bijection.

Proof: For arbitrary $x,y \in [0,1)$ with $x \neq y$ it follows that $\mathrm{id}(x) = x \neq y = \mathrm{id}(y)$. Therefore, $\mathrm{id}$ is injective. For an arbitrary $y \in [0,1)$ there is always an $x \in [0,1)$, such that $y = \mathrm{id}(x)$, namely $x := y$. Therefore, $\mathrm{id}$ is surjective. Since $\mathrm{id}$ is both injective and surjective, it is bijective.