Is there any other function $f(x)$ such that $f$ is Discontinous at $x=a$ but $fof$ is continous Is there any other function $f(x)$ such that $f$ is Discontinous at $x=a$ but $fof$ is continous.
I know the well know example for this as Dirchlet's function. is there any other?

$f$ defined on $\mathbb{R}$ by $f(x)=1$ if $x\leq 0, f(x)=2$ if $x>0$. $f$ is discontinuous at $0$ and $f\circ f$ is continuous at $0$.
