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Math Help - Extended function

  1. #1
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    Extended function

    Let F(x) = [(x + 3x -4) / (x - 4x + 3)]

    Give a formula for the extended function that is continuous at x=1
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  2. #2
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    Quote Originally Posted by h4hv4hd4si4n View Post
    Let F(x) = [(x + 3x -4) / (x - 4x + 3)]

    Give a formula for the extended function that is continuous at x=1
    Notice that

    \frac{x^2 + 3x -4}{x^2 - 4x + 3} = \frac{(x+4)(x-1)}{(x-3)(x-1)}

    so the terms (x-1) will cancel provided that x \ne 1

    So let us define the extended function G(x) such that

    G(x) = \left\{\begin{array}{cc}\frac{x+4}{x-3},&\mbox{ if }<br />
x \ne 1\\- \frac{5}{2}, & \mbox{ if } x=1.\end{array}\right.
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  3. #3
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    thanks so much!
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