Let $f:ℂ→ℝ$ be a non-analytic function. Let $h(s)=f(a+s)$, where $a∈ℝ$. If $h$ is an odd function, then $(0,0)$ is a symmetric point for $h$ (the graph of $f$ is symmetric with respect to the origin). Is it true that the point $(a,0)$ is a symmetric point for $f$?
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