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Math Help - continuous function

  1. #1
    Super Member
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    continuous function

    how do you prove this:

    let f: real numbers -> real numbers be continuous and bounded and define g as g(x) = sup {f(x) : y< x}. prove that g is continuous.

    this is what i did:

    i wrote the def of continuous function for f, assuming that f is cont at the pt c and then i got stuck..
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  2. #2
    Senior Member Tinyboss's Avatar
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    The function g is monotone--what kinds of discontinuities can a monotone function have?
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