Thanks in advance for the help.

definition: a function f is said to cover the set M if for every point y in M there is an x in the domain of f so that f(x)=y.

Prove: Suppose that f is continuous with domain [a,b] so that f(x) is in [a,b] for every x in [a,b]. Prove that there is some x in [a,b] so that f(x)=x.