Don't we first have to solve for the midpoint, f(x)=f(2-x), so 2x=2, 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.)
Yes, you're correct! Since we have \(f(x)=f(2-x)\), \(2x=2, x=1.\)