Continuous Function with Open Range

[Ted123]

What is an example of a continuous function $f:\mathbb{R}\to\mathbb{R}$ such that $f(\mathbb{R})$ is open?

 

[CompuChip]

Well, $\mathbb{R}$ is open in $\mathbb{R}$, right?

 

[Ted123]

Well, $\mathbb{R}$ is open in $\mathbb{R}$, right?

So $f(x)=x$ is open