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Math Help - Intersection of Functions

  1. #1
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    Intersection of Functions

    I need help finding the points at which the following 2 functions intersect:

    f(x) = 1/x
    g(x) = -x^2 + 4x - 2

    for x>0

    I figured out that x=1 was a solution, by inspection, but I cannot solve for the other one.
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by kaiser0792 View Post
    I need help finding the points at which the following 2 functions intersect:

    f(x) = 1/x
    g(x) = -x^2 + 4x - 2

    for x>0

    I figured out that x=1 was a solution, by inspection, but I cannot solve for the other one.
    calculate the equation for

    f(x) = g(x)
    so,
    \frac{1}{x} = \frac{{-x^2}+4x-2}{1}
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  3. #3
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    I realize that I need to set f(x) equal to g(x), but I'm not able to solve the resulting equation for x.
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  4. #4
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    \frac{1}{x} = -x^2 + 4x - 2

    1 = -x^3 + 4x^2 - 2x

    0 = -x^3 + 4x^2 - 2x - 1

    0 = x^3 - 4x^2 + 2x + 1

    Clearly we need to factor the right-hand side to find the solutions. You already know (x-1) is a factor because you said that x=1 is a solution. So, use polynomial long division (or synthetic division) to factor and find the other solutions.
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  5. #5
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    Thanks, I forgot about dividing out the known factor.
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