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Math Help - calc help

  1. #1
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    calc help

    f(x) = {(x^2-4)/(x-2) if x<2}
    {ax^2-bx-3 if 2<x<3}
    {2x-a+b if x >= 3}

    They are all part of the same function...the problem is to find the values of a and b to make the entire function continuous. I got a and b is equal to .5, could anyone help me on this please?

    thanks.
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  2. #2
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    Quote Originally Posted by amma0913 View Post
    f(x) = {(x^2-4)/(x-2) if x<2}
    {ax^2-bx-3 if 2<x<3}
    {2x-a+b if x >= 3}

    They are all part of the same function...the problem is to find the values of a and b to make the entire function continuous. I got a and b is equal to .5, could anyone help me on this please?

    thanks.
    Note that \frac{x^2 - 4}{x - 2} = x + 2 for x \neq 2.

    So for continuity at x = 2 you require the following: 2 + 2 = 4a - 2b - 3.

    For continuity at x = 3 you require 9a - 3b - 3 = 6 - a + b.

    Simplify each of the above equations and solve them simultaneously for a and b.
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