1. The problem statement, all variables and given/known data Given a function such that [itex]f(x)=f(a-x)[/itex] where a is some constant, what can we say about this function? This isn't actually homework; so please forgive the fact that I'm being a little vague 2. Relevant equations None. 3. The attempt at a solution I think that a periodic function (with period a) which is also even satisfies this but is there something else that can also satisfy this condition? Not really sure how to proceed in proving either that this is the only answer or to show an alternative.