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Math Help - A rational function is not continuous

  1. #1
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    A rational function is not continuous

    Show that f is not continuous at x (see diagram).
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    Having trouble with this for a while, thanks..
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  2. #2
    Senior Member Tinyboss's Avatar
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    Pick any rational x. Then f(x) is nonzero. There are irrational numbers arbitrarily near to x. Can you finish from there?

    Edit: By the way, "rational function" is the name for a different kind of function from this one, namely one that is the quotient of two polynomials.
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  3. #3
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    thanks, i read the proof regarding Q and R in my book, but i still dont really know how to answer it, any more tips? Thanks!
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  4. #4
    Senior Member Tinyboss's Avatar
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    Write the definition of "f is continuous at x" (the one with epsilon and delta), then show that the definition does not hold for x rational, for the reason I gave. Try setting epsilon = f(x)/2.
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  5. #5
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    thanks, i'll try it out..
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