Mapping/Squaring/Image and preimage/Example

For the mapping

$\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto x^{2},$

the image of ${}[1,2]$ is the set of all squares of real numbers between ${}1$ and ${}2$, this is thus ${}[1,4]$. The preimage of ${}[1,4]$ consists of all real numbers whose square is between ${}1$ and ${}4$. This is ${}[-2,-1]\cup [1,2]$.