Hi people,

f is a continuous function in $\displaystyle \mathbb{R}$ such as:

$\displaystyle (\forall x \in \mathbb{R}) \ \ f(2x)=f(x)$

I showed that $\displaystyle (\forall \alpha \in \mathbb{R}) \ \ (\forall n \in \mathbb{N}) \\f(\frac{\alpha}{2^n})=f(\alpha)$, but idon't know how to deduct that

f is constant????