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Math Help - finding intersection of two functions

  1. #1
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    finding intersection of two functions

    Here are the functions:

    (G of k)(x) = x^2-1

    f(x) = x^2/(x^2+1)


    how do i find the intersecrions?
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  2. #2
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    Quote Originally Posted by Anemori View Post
    Here are the functions:

    (G of k)(x) = x^2-1

    f(x) = x^2/(x^2+1)


    how do i find the intersecrions?
    Start by solving x^2 - 1 = \frac{x^2}{x^2 + 1}.
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    Quote Originally Posted by Anemori View Post
    Here are the functions:

    (G of k)(x) = x^2-1

    f(x) = x^2/(x^2+1)


    how do i find the intersecrions?
    The values of the functions must be equal at the point of intersection. Thus:

    x^2-1=\dfrac{x^2}{x^2+1}

    Multiply both sides by x^2+1 to get rid of the fraction and move all terms to the LHS:

    x^4-x^2-1=0

    This is a quadratic equation in x. Use the substitution u = x^2~\implies~|x|=\sqrt{u}. The equation becomes:

    u^2-u-1=0

    Solve for u, afterwards determine x, plug in the value of x in one of the equations of a function to calculate the y-coordinate of the point of intersection.
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