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Continuous Function

  1. Aug 20, 2008 #1
    Q.

    Determine the constants a and b so that the function is continuous on the entire real line.

    2 if x <= -1
    f(x) = ax+b if -1 < x < 3
    -2 if x >= 3

    Ans:

    a = 1; b = -1

    I wonder if the answer is right??
     
  2. jcsd
  3. Aug 20, 2008 #2

    tiny-tim

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    Almost … check it again … :wink:
     
  4. Aug 20, 2008 #3
    Which one is wrong, a or b, or both??
     
  5. Aug 20, 2008 #4
    Suppose your answer IS correct, that would mean

    2 if x <= -1
    f(x) = x - 1 if -1 < x < 3
    -2 if x >= 3

    However when x = -1, you get 2 (from the criterion x <= -1) and -2 for the criterion -1 < x < 3. Also when x = 3, you get 2 for the criterion -1 < x < 3 and -2 for the criterion x >= -3. You don't want those jumps if your f is cont.
     
  6. Aug 20, 2008 #5

    nicksauce

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    Exactly. You shouldn't have to "wonder" if your answer is correct, you can check it yourself. Is the left-side limit of f(x) equal to the right-side limit at x=-1? at x = 3?
     
  7. Aug 20, 2008 #6
    you have 2 linear equations with 2 unknowns

    -a + b = 2
    3a + b = -2
     
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