continuous function, point in set
Let ![f: [a,b] \rightarrow [a,b]](http://latex.codecogs.com/png.latex?f: [a,b] \rightarrow [a,b])
be a continuous function. Prove that there is at least one point ![x \in [a,b]](http://latex.codecogs.com/png.latex?x \in [a,b])
so that =x)
.
This looks a lot like Intermediate Value Theorem but with the condition that . The condition that is tricky for me, that there is an that satisfies this. Thanks for any help.
