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