Is it true that if f:[0,1]→[0,1]f : [0,1] \to [0,1]f:[0,1]→[0,1] is
a) monotone increasing
b) monotone decreasing
then there exists an x∈[0,1]x \in [0,1]x∈[0,1] for which f(x)=xf(x) = xf(x)=x?
Hidden so you can work on the problem first.