R to R/Linear/Mapping/Example

Let ${\displaystyle {}a\in \mathbb {R} }$ be fixed. This real number defines a mapping

${\displaystyle \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto ax.}$

For ${\displaystyle {}a=0}$, this is the constant zero mapping. For ${\displaystyle {}a\neq 0}$, we have a bijective mapping; the inverse mapping is

${\displaystyle y\longrightarrow {\frac {1}{a}}y.}$

Here, the inverse mapping has a similar form as the mapping itself.