Let $D \subset \mathbb{C}^k$ be your favorite complex domain. Suppose we are given a proper holomorphic mapping $f \colon D \to \mathbb{C}^{k+2}$.

Let us take $k+1$ generic linear functions $l_i \colon \mathbb{C}^{k+2} \to \mathbb{C}$, $i = 1,\ldots,k+1$ and form a linear map $L \colon \mathbb{C}^{k+2} \to \mathbb{C}^{k+1}$ by $L := (l_1, \ldots, l_{k+1})$.

Is it true that $L \circ f$ is proper as well? How one can show that?

I understand that mathstackexchange is more appropriate place for such a question. I just feel like leave it here.