Given a linear form f on vector space L, prove that there exists one-dimensional subspace M such as L is direct sum of Ker f and M

Question

Reading my linear algebra professor's lectures I've stumbled upon following question:

Suppose we are given a non-zero linear form $f$ on vector space $L$. Prove that there exists one-dimensional subspace $M \subset L$, $dim M = 1$, such as that $L$ is a direct sum of $Kerf$ and $M$: $$L = Kerf ⊕ M$$

Firstly I dont even really understand the question, after all saying there exists such M for all $f$ at the very least would imply that the $dimKerf = dimL - 1$, which is clearly not true (at least for any given $f$). Am I missing something here ?