  We study the point pair function in subdomains $G$ of $\mathbb{R}^n$. We
prove that, for every domain $G\subsetneq\mathbb{R}^n$, the this function is a
quasi-metric with the constant less than or equal to $\sqrt{5}\slash2$.
Moreover, we show that it is a metric in the domain
$G=\mathbb{R}^n\setminus\{0\}$ with $n\geq1$. We also consider generalized
versions of the point pair function, depending on an arbitrary constant
$\alpha>0$, and show that in some domains these generalizations are metrics if
and only if $\alpha\leq12$.
