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Math Help - inverse functions

  1. #1
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    inverse functions

    i need to find the inverse of f(x) = x^2-4x+3 how do you do it when you have x^2 and x?
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  2. #2
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    Quote Originally Posted by katt View Post
    i need to find the inverse of f(x) = x^2-4x+3 how do you do it when you have x^2 and x?
    complete the square.
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  3. #3
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    Y=x^2-4x+3 => x^2-4x+3-y=0

    delta'=4-3+y=1+y

    => x1=2+squareroot(1+y)
    and x2=2-squareroot(1-y)

    this is the inverse you choose x1 or x2 depending on the constrains given .
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  4. #4
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    y = x^2 - 4x + 3<br />

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

    y = (x - 2)^2 - 1

    swap x and y ...

    x = (y - 2)^2 - 1

    x + 1 = (y - 2)^2

    \pm \sqrt{x+1} = y - 2

    y = 2 \pm \sqrt{x+1}

    restrict the domain of the original function to x \ge 2, and the inverse function is f^{-1}(x) = 2 + \sqrt{x+1}<br />
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