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Confusion about continuity question.

  1. Oct 13, 2012 #1
    1.The Question

    The function f(x)=


    x2/x if (x≠0)



    0 if(x=0)










    3. The attempt at a solution


    I thought this had a removable discontinuity at x=0, because the function s2/x is not defined at x=0, and the expression can be reduced to x.

    The book (one of those AP prep guides with solutions) says that it is continuous everywhere, to note that x2/x if x≠0 and lim(x->0) f = 0.

    Why was I wrong?

    Thanks in advance.
     
  2. jcsd
  3. Oct 13, 2012 #2

    SammyS

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    The function g(x) = x2/x does have a removable discontinuity at x=0.

    The piecewise function, f(x) that you give has that discontinuity removed. f(x) is defined for all x, and is continuous for all x, even for x = 0.
     
  4. Oct 13, 2012 #3
    SammyS

    Thanks so much for your quick response.


    So, just to be sure, once the discontinuity is removed, the function is continuous everywhere, is that right?

    Thanks again.
     
  5. Oct 13, 2012 #4

    SammyS

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    Yes, that's right.
     
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