Example of inverse does not equal the argument

Question

Let $f:A\rightarrow B$. For all subsets $N$ of $A$ it follows that

$N\subseteq f^{-1}(f(N))$

Problem: Show an example that $f^{-1}(f(N))$ does not necessarily equal $N$

My idea: Would it be sufficient to let $A=\left \{ 0,1 \right \}$ and $B=\left \{ 0\right \}$ and then be done? The inverse notation on a set is kind of messing with me.