# Showing that the composition of maps of constant rank does not have to be of constant rank

This is an exercise from p.79 of John Lee's Introduction to Smooth Manifolds. I am trying to search the smooth maps of the Euclidean space but cannot find a counterexample... Could anyone please suggest me one?

The map$f:\mathbb R\to \mathbb R^2:t \mapsto (t,t^2)\;$ has rank one everywhere.
The map $g:\mathbb R^2 \to \mathbb R:(x,y)\mapsto y\;$ has rank one everywhere.
Nevertheless the map $g\circ f:\mathbb R \to \mathbb R:t\mapsto t^2$ rank $1$ at $t\neq 0$ but rank $0$ at $t=0$ .