Let f: [0,1] to R(eal numbers) be a function that maps closed and bounded interv

Question

Let f: [0,1] to R(eal numbers) be a function that maps closed and bounded intervals onto closed and bounded intervals, hence if 0 <(or equal to) a < b <(or equal to) 1, then for some real numbers c <(or equal to) d, f([a,b]) = [c,d].

a.I have already: Proved there is a x-knot belonging to [0,1], such that for all x belonging to [0,1], f(x) <(or equal to) f(x-knot).
b. I have already: Proved the range of f has the intermediate value property.

c. So i need to: Give an example showing f need not be continuous. Any ideas??

Explanation / Answer

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