The function is odd.
Work Step by Step
We have that $E(-x)=E(x)$ and $O(-x)=-O(x)$. Let $\Phi=O\circ O$ Then $$\Phi(-x)=O\circ O(-x)=O(O(-x))=O(-O(x))=-O(O(x))=-O\circ O(x)=-\Phi(x)$$ which means that the function is odd.
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