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If $f(x)=f(2-x)$ for all $x$, then what line is necessarily an axis of symmetry of the graph of $y=f(x)$? (Give the simplest equation of this line.)

 Feb 24, 2021
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We claim that it's $\boxed{x=1}$.

Notice that $f(1)=f(1)$, and $f(1+k)=f(1-k)$, implying the answer.

 Feb 24, 2021

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