Let f:[a,b] --> R be a continuous function such that [a,b] is a subset of [f(a), f(b)]. Prove that there exists x* in [a,b] such that f(x*)=x*
Hm, I'm not following you... how will that help me prove f(x*)=x* for some x*?
I understand the "geometry" of the problem, ie, the function is "taller" than it is "wide" so the line y=x must pass through the function. Just having a difficult time proving that.