duplicates 557764: Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$ and 1030029: Prove $F(F^{-1}(B)) = B$ for onto function seem like duplicates to me.

I'd say answers to 1030029 are a bit better. OTOH some users might be inclined to close this one for the lack of context. (Although the attempt shown in the older one does not amount to much, either.) In which direction to close?