Proving a fixed point on a function

[bluevires]

Hello guys, this question is kinda bothering me since I'm having trouble with one of the steps in proving it.

The question reads. Assume funciton f is continuous on an interval [0,1], such that the range of f is contained within or equal to [0,1]. Show that for a value of c contained within [0,1] there exists f(c)=c.

I know that the proof process must involve the use of Intermediate Value Theorem, but I can't seem to find a way to show that
k = c, (k is a arbitrary number contained within [0,1].

Any tips /help would be appreciated

 

[AKG]

Show that for a value of c contained within [0,1] there exists f(c)=c.

That can't possibly be what your question says. Doesn't it say "show that there exists some c in [0,1] such that f(c)=c"? Consider the function g(x) = x-f(x) and apply IVT.

 

[bluevires]

Thank you AKG, problem solved ^^

I had a similar idea but both worked out ok.