Assume that $f\colon\mathbb{E}\subset\mathbb{R}\rightarrow\mathbb{R}$, $f(x)=\max\lbrace2x-5,x-2\rbrace$.
Determine $\mathbb{E}$ for which $f$ is a bijection.
I was thinking it is $\mathbb{R}$, but I'm not sure. Can I get a confirmation and a way to prove it, please? Thank you very much!