I see that you have severval other postings.
You should understand that this is not a homework service nor is it a tutorial service.
PLease either post some of your own work on this problem or explain what you do not understand about the question.
Plx helpa) Let f :[a,b] --> [a,b] be continuous on [a,b]. Prove that f has a fixed point, i.e., prove that (exist) c in [a,b] such that f(c)=c
b) let f,g : [a,b]->[a,b] be two continuous function on [a,b] such that f(a)>or equal g(a) and f(b)<or equal g(a).
Prove that exist c in [a,b] such that f(c) =g(c)
Go to your textbook and class notes and review examples that apply the Intermediate Value Theorem. Spend more than just a few minutes doing this. Then come back if you still have this question. (You will find that the question you posted is a standard example in many textbooks that cover this material).
So you are saying that I should prove that f(c)is not > or < c is equal c ?
Or saying I did find out f(c)=0 since it equal 0 so that is a c exist?
I am so confused abt this because when I was doing that first I did prove that that f(c)is not > or < c is equal c. Then I thought I get it wrong because what I am doing is proving that IVT is true. That's why I use the other way, to use g(a)<0<g(b) find out that f(c)= 0.
Thanks