Hello,

I have a following problem to solve:

For some function $\displaystyle f:X \rightarrow Y$ and $\displaystyle C \subseteq Y$ I have to find something, that would equal $\displaystyle f(f^{-1}(C)) = ?$.

I managed to show that $\displaystyle f(f^{-1}(C)) \subseteq C$ and I have a counterexample that disproves $\displaystyle C \subseteq f(f^{-1}(C)) $. Yet I have no idea what $\displaystyle f(f^{-1}(C))$ could equal to.