Work Step by Step
We know that if a function is odd, then $f(-x)=-f(x).$ So here $f(x)=-f(x)$ and $g(x)=-g(x)$. Then $f(g(x))=f(-g(x))=-f(g(x))$, thus $f(g(x))$ is also odd, thus we proved what we had to.
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