suppose f: [a,b] ->R is increasing and for every Y in [f(a), f(b)], there is some x0 in [a,b] such that f(x0) = Y I want to show that f is a continious function but dont know how to go about this problem , can some one please help ..thanks
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Originally Posted by dopi suppose f: [a,b] ->R is increasing and for every Y in [f(a), f(b)], there is some x0 in [a,b] such that f(x0) = Y I want to show that f is a continious function but dont know how to go about this problem , can some one please help ..thanks If is strictly increasing and maps intervals into intervals. Then must be continous. Use the above fact to prove this partial conversve of the intermediate value theorem.
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