DSE 2020 Question 38: Real analysis

Suppose the distance between $x,y\in\mathbb{R}$ is $|x-y|$ and $f:\mathbb{R}\to\mathbb{R}$ is continuous. If $E$ is an open subset of $\mathbb{R}$, then $\{x\in\mathbb{R}\mid f(x)\in E\}$ is