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Math Help - problem on continuity and differentiability

  1. #1
    Senior Member Sambit's Avatar
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    Question problem on continuity and differentiability

    Let, f(x) = x , if x is rational
    = 0 , if x is irrational.

    Then at x=0, which one of he followings is true?
    (a) both f and  f^2 are differentiable
    (b) neither f nor  f^2 are differentiable
    (c)  f^2 is continuous but not differentiable
    (d)  f^2 is differentiable but f is not

    please help.
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by Sambit View Post
    Let, f(x) = x , if x is rational
    = 0 , if x is irrational.

    Then at x=0, which one of he followings is true?
    (a) both f and  f^2 are differentiable
    (b) neither f nor  f^2 are differentiable
    (c)  f^2 is continuous but not differentiable
    (d)  f^2 is differentiable but f is not

    please help.
    This is the well-known Dirichlet function: Math Tutor - Functions - Theory - Elementary Functions
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  3. #3
    Senior Member Sambit's Avatar
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    ya, but what about f^2?
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    Modification 2.
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  5. #5
    Flow Master
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    Quote Originally Posted by Sambit View Post
    ya, but what about f^2?
    I have provided you with a reference. You are now expected to think.
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  6. #6
    Senior Member Sambit's Avatar
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    yes i understood.
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