How can we prove that for every $\alpha,$ $\alpha \in aut(\mathbb Q)$ has the form $\alpha(x)=x\alpha(1)?$

Question

How can we prove that for every $\alpha,$$\alpha \in aut(\mathbb Q)$ has the form $\alpha(x)=x\alpha(1)?$

My try: It looks obvious but no idea of proof.