Because f(x)=f(2a-x), for any t point in the domain, there is f(t)=f(2a-t), that is, there is a 2a-t point, which makes the function values of these two points equal.

And [t+(2a-t)]/2=a, that is, the midpoint of these two points is a, we get:

For any point t, there is a symmetric point 2a-t about a, so f(x) is symmetric about x = a.