I need some help with proving that $$f(x)=\sqrt[3]{x}+2$$ is a contraction mapping $(f: \mathcal{R} \rightarrow \mathcal{R})$. So I need to show that there exist $\alpha\in (0,1)$ such that for all $x,y$ $$|f(x)-f(y)|\leq \alpha|x-y|.$$
I have nothing so I need any help. Thank you!