CN-LEAGUE 2012 Problem 6

Let $f(x)$ be an odd function on $\mathbb{R}$ , such that $f(x)=x^2$ when $x\ge 0$ . Knowing that for all $x\in [a,a+2]$ , the inequality $f(x+a)\ge 2f(x)$ holds, find the range of real number $a$ .