Composition/Continuous function followed by staircase function/No staircase function/Exercise

Give an example of a continuous function

$f\colon [a,b]\longrightarrow [c,d]$

and a staircase function

$g\colon [c,d]\longrightarrow \mathbb {R}$

such that the composite ${}g\circ f$ is not a staircase function.

Create a solution