1. Suppose that f and g are continuous functions defined on R and every interval (a, b) contains some point y with f(y) = g(y). Show that f(x) = g(x) for every x in R. 3. I can show that between any two points in are there is some x such that f(x)=g(x). Is that enough? I don't think it is but have no idea what else I can do. Any ideas?