Let f:[0,1]to[0,1] be defined as follows: f(x)=begincasesx, & xinmathbb Qcap[0,1], x+frac23, & xinmathbb Q^Ccap(0,frac13), x-frac13, & xinmathbb Q^Ccap(frac13,1).endcases Which of the following statements is (are) TRUE?

Q33Section B (Section B)33 of 60

A bijection of the unit interval defined by rationality

Let $f:[0,1]\to[0,1]$ be defined as follows:

$f(x)=\begin{cases}x, & x\in\mathbb Q\cap[0,1],\ x+\frac23, & x\in\mathbb Q^C\cap\left(0,\frac13\right),\ x-\frac13, & x\in\mathbb Q^C\cap\left(\frac13,1\right).\end{cases}$

Which of the following statements is (are) TRUE?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

Keyboard: A–D answer · S solution · ←/→ previous/next