Let $f \colon \mathbb{R}→ \mathbb{R}$ be a continuous function.Which of the following is always true?
1. $f ^{-1}(U)$ is open for all open sets $U ⊆\mathbb{R}$
2. $f ^{-1}(C)$ is closed for all closed sets $C ⊆\mathbb{R}$
3. $f ^{-1}(K)$ is compact for all compact sets $K⊆ \mathbb{R}$
4. $f ^{-1}(G)$ is connected for all connected sets $G ⊆ \mathbb{R}$
1 and 2 are always true but i am not sure about the others.can somebody help me