Let E be a closed set, then$ E= f^{-1} ({0})$ for an$ f: \Bbb R^p \rightarrow \Bbb R$ continuous

Question

Alright, I understand what it means, that for a closed set $E$ that lies in $A$, (a vectorial space), you can always find a continuous function such as every element of the closed set $E$ ends up in the zero from the vectorial space $B$, where $f(E)=0$. But my trouble with this problem is that in particular in order to prove this I need to define a function that is continuos and that its inverse image for the set $\{0\}$ is the same as $E$. But how can I describe a general function that works for every closed set that I can imagine, that respects the theorem. I just want some tips to begin, because i found pretty hard to imagine a general function such as the one that they ask me.