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Math Help - determining a and b

  1. #1
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    determining a and b

    f(x)= 2x-1. 1<x<3
    f(x)= x^2+ax+b, lx-2l greater than or equal to 1

    so i know that the absolute value means x is greater than or equal to 3 and x is also less than or equal to 1.

    so are the answers:
    a=-2 and b=2?
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  2. #2
    MHF Contributor
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    Is the question:

    What are the values of a and b that make f(x) a continuous function?
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  3. #3
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    yes. sorry i forgot to add that
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  4. #4
    MHF Contributor
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    Ok, then you need the limit of the function to be the same when x approaches 1 from the left and from the right, and also the same when x approaches 3 from the left and from the right.

    This means

    2x - 1 = x^2 + ax + b when x = 1 and when x = 3.

    Substituting those values of x into the equation, we get these two equations:

    2(1) - 1 = 1^2 + a(1) + b

    2(3) - 1 = 3^2 + a(3) + b

    Simplifying, we get

    a + b = 0

    3a + b = -4

    a = -2, b = 2

    You are correct.
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