Easy# The Euclidean norm applied to a function may generate a metric

TOPO-WV1BB4

Let $f:\mathbb{R}\to \mathbb{R}\,$ and define $f:\mathbb{R} \times \mathbb{R}\to \mathbb{R}$ by:

$$ d(x,y)=|f(x)-f(y)|, \ x,y\in \mathbb{R}$$

You are told that $\,d\,$ is a metric.

What is necessarily **TRUE** about $f\,$?