Continuous Function

  • Thread starter Loppyfoot
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Homework Statement


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?
 
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Answers and Replies

  • #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.
 
  • #3
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But when b=4, the top x^2-4 and the bottom x^2-4 cancel out to leave x-1.
 
  • #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.
 
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So are there any values of b that make this function continuous?
 
  • #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?
 
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So there are no values of b that makes this function continuous?
 
  • #8
LCKurtz
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That makes it continuous for all x, which is what was required.
 
  • #9
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Alright, thanks LC!
 

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