$f(x)=\left\{\begin{matrix}x,&x\,is\,rational\\1-x,&x\,is\,irrational\end{matrix}\right.$, then at $x=\frac{1}{2}$, f(x) is

continuous but non-differentiable discontinuous differentiable none of these

continuous but non-differentiable

$f(\frac{1}{2})=\frac{1}{2},\underset{x→\frac{1} {2}}{\lim}f(x)=\frac{1}{2}$. But $f'(\frac{1}{2})$ is not well defined.