MathNet 2012 Question 27

Let $f(x)$ be an odd function on $\mathbb{R}$, and $f(x) = x^2$ for $x \ge 0$. Suppose for any $x \in [a, a+2]$, $f(x+a) \ge 2f(x)$. Then the range of real number $a$ is ______.