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Math Help - Analysis question no.2

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    Analysis question no.2

    if we know that f : [a,b] ----> reals is continuous. How can we prove that the image f([a,b]) is a closed interval say [m,M] for some m,M in reals?
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    A continuous function maps a compact set to a compact set.
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    Quote Originally Posted by maximus101 View Post
    if we know that f : [a,b] ----> reals is continuous. How can we prove that the image f([a,b]) is a closed interval say [m,M] for some m,M in reals?

    Or, perhaps a little simpler answer than HallsofIvy's, put f(a)=m\,,\,f(b)=M and now use the

    intermediate value theorem for continuous functions...

    Tonio
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