# Continuous function/Closed interval/Continuous Continuation/Exercise

Let

${\displaystyle f\colon [a,b]\longrightarrow \mathbb {R} }$

be a continuous function. Show that there exists a continuous extension

${\displaystyle {\tilde {f}}\colon \mathbb {R} \longrightarrow \mathbb {R} }$
of ${\displaystyle {}f}$.