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Math Help - Continuity of a Piecewise Function

  1. #1
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    Continuity of a Piecewise Function

    Let f: R->R be defined by
    f(x)={x2 for x in Q, x+2 for x not in Q}

    Find all points (if any) where f is continuous.

    We learned that a function is continuous at a point where f(x)=limit as x->p f(x). I'm just not really sure how to go about finding these.

    I think for all x in Q this function is discontinuous for all x not equal to zero, since that will be only case where f(x) will equal its limit. Is this correct thinking?
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    Re: Continuity of a Piecewise Function

    Quote Originally Posted by renolovexoxo View Post
    Let f: R->R be defined by
    f(x)={x2 for x in Q, x+2 for x not in Q}
    Find all points (if any) where f is continuous.
    Is f continuous at x=2~?
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    Re: Continuity of a Piecewise Function

    f is continuous at the points satisfying x^2=x+2
    Thanks from renolovexoxo
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