Bijection mapping
Trivia · proposed by @vipproaccout
Which of the following maps is a bijection?
A$f:\mathbb{R}\to\mathbb{R}$, $\;f(x)=\begin{cases}0 & \text{if } x\in\mathbb{Q},\\ 1 & \text{if } x \text{ is irrational.}\end{cases}$
B$f:\mathbb{R}\to\mathbb{R}$, $\;f(x)=x^2-1$ for all $x\in\mathbb{R}$.
C$f:\mathbb{Z}\to\mathbb{Z}$, $\;f(2n)=2n$ and $f(2n+1)=n$ for all $n\in\mathbb{Z}$..
D$f:\mathbb{R}\to\mathbb{R}$ satisfying $f(2f(x))=x^3$ for all $x\in\mathbb{R}$.