Solution
= Solution
Take the <step function>
$$
\boxed{f_3(x)=\begin{cases}0,&0\le x<1/2,\\1,&1/2\le x\le1.\end{cases}}
$$
It is bounded between zero and one, and is discontinuous at $x=1/2$.
= Solution
Take the <step function>
$$
\boxed{f_3(x)=\begin{cases}0,&0\le x<1/2,\\1,&1/2\le x\le1.\end{cases}}
$$
It is bounded between zero and one, and is discontinuous at $x=1/2$.