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Continuous Function

  1. Sep 24, 2009 #1
    1. The problem statement, all variables and given/known data
    For what positive values of b is f continuous for all real numbers x?
    f(x) = ((x-1)(x2-4))/(x2-b)

    So I go one value of b for the function to be continuous. I got that b=4. How do I find any others? If there even are any others?
     
    Last edited: Sep 24, 2009
  2. jcsd
  3. Sep 24, 2009 #2

    LCKurtz

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    I suppose you mean "a", not "b". And no, if a = 4 it isn't continuous for all values of x because then it is an undefined 0/0 form when x = ±2. And if you cancel the offending factors it is no longer the same function.
     
  4. Sep 24, 2009 #3
    But when b=4, the top x^2-4 and the bottom x^2-4 cancel out to leave x-1.
     
  5. Sep 24, 2009 #4

    LCKurtz

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    Yes, but they are no longer the same function since they don't have the same domain. For example consider the function y = x/x. This is not defined when x = 0, so its domain is x ≠ 0. But if you cancel the x's you have y = 1 which is defined for all x. The two functions do not have the same domain so they are not the same function.
     
  6. Sep 24, 2009 #5
    So are there any values of b that make this function continuous?
     
  7. Sep 24, 2009 #6

    LCKurtz

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    I think you know the answer. You would need a positive b (positive was given) so (x2-b) never gives you a zero in the denominator for any x, eh?
     
  8. Sep 24, 2009 #7
    So there are no values of b that makes this function continuous?
     
  9. Sep 24, 2009 #8

    LCKurtz

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    That makes it continuous for all x, which is what was required.
     
  10. Sep 24, 2009 #9
    Alright, thanks LC!
     
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