The $Homeo(\mathbb{R})$ be the group of all the homeomorphisms on $\mathbb{R}$, with the group operation of composition. Let $f(x)=x^3+\alpha$ and $g(x)=x^3+\beta$ be two elements of $Homeo(\mathbb{R})$ with $\alpha$ and $\beta$ two rationally independent irrational number. Then we consider the subgroup $G$ of $Homeo(\mathbb{R})$ generated by $f$ and $g$. My question is that is $G$ a free group?
Thanks for any help.