I notice that the function $f(x)$ is symmetric about the line $x=1$, since replacing $x$ with $2-x$ does not change the value of $f(x)$. That means that the line $x=1$ is an axis of symmetry of the graph of $y=f(x)$. The simplest equation of this line is just $x=1$.


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.)