Let $f:M \longrightarrow N$ be a module homomorphism and let $L$ be a submodule of $M$. I would like to prove that
$f^{-1}f(L)=L+\text{Ker}f.$
I tried using the first isomorphism theorem, but I cannot write it for the inverse function $f$. Is it the right approach? What is the best way to prove it?