Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere?
I found this question here, the question seems much interesting but for obvious reason it is closed there, I was wondering how to derive such a function?
Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere?
I found this question here, the question seems much interesting but for obvious reason it is closed there, I was wondering how to derive such a function?
You could take $f(x)=\begin{cases}1&x\in \mathbb Q \\ -1&x\in\mathbb R\setminus\mathbb Q\end{cases}$