My exercise says: Let $f:\mathbb{R} \rightarrow \mathbb{R}$ a continuous function e suppose that exists $k$ such that:
$|f(x)-f(y)|\geq k|x-y|$
Then $f$ is bijective and its inverse is continuous.
Well, there's a Theorem , Invariance of domain, that says
"If $U$ is an open subset of $\mathbb {R^n}$ and $f : U \rightarrow\mathbb{R}$ is an injective continuous map, then $V = f(U)$ is open and $f$ is a homeomorphism between $U$ and $V$".
But I'm not knowing how to proceed...need a clue...Thanks for attention!!!