1. The problem statement, all variables and given/known data Suppose the g:[0,1] -> R is continuouse, with g(0)=g(1). Show that there exists an x in [0,1/2] such that g(x) = g(x+1/2) 2. Relevant equations The intermediate value theorem is used in there somewhere. IVT: If f(x) is continuous on the interval [a,b] and f(a)<q<f(b), then there exists an x in [a,b] such that f(x)=q. 3. The attempt at a solution I tried creating another function, p(x) = g(x) - g(x+1/2). I want to show p(x)=0 at some point in [0,1/2] by finding a positive number in the interval and a negative one, then quote the IVT. But I can't seem to do that. I tried substituting the endpoint values in but they didn't help much. And I assume that g(0)=g(1) must come into play somewhere?