Using the Intermediate Value Theorem to Find Fixed Points

[JasMath33]

Homework Statement

Homework Equations

The Attempt at a Solution

I started looking at this problem and I think I am going to have to use the intermediate value theorem for this proof, but I am not quite sure. I started looking at possible examples of these functions, but I know this is not good enough for proofs.

 

[BiGyElLoWhAt]

https://en.wikipedia.org/wiki/Fixed-point_theorem
have you tried this?

There's a list of a lot of fixed point theorems. Most of which include rewriting the function as ||f(x)-x|| = 0 and looking for the roots of the equation.

 

[JonnyG]

Check out the Banach fixed point theorem.