Let $f : \mathbb{C} \longrightarrow \mathbb{C}$ be a holomorphic function. Choose the correct statement(s) from below:\\
(A) $f(\bar{z})$ is holomorphic;\\
(B) Suppose that $f(\mathbb{R}) \subseteq \mathbb{R}$. Then $f(\mathbb{R})$ is open in $\mathbb{R}$;\\
(C) the map $z \mapsto e^{f(z)}$ is holomorphic;\\
(D) Suppose that $f(\mathbb{C}) \subset \mathbb{R}$. Then $f(A)$ is closed in $\mathbb{C}$ for every closed subset $A$ of $\mathbb{C}$.