Math

Find the Inverse Function:

y=4x-x^2

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  1. You were given:

    y = 4x - x^2

    We switch x and y.

    x = 4y - y^2

    Factor the right side of the equation.

    x = y(4 - y)

    Next:

    xy = 4 - y

    Add y on both sides of the equation.

    xy + y = 4

    Factor on the left side.

    y(x + 1) = 4

    Isolate y on the left side.

    y = 4/(x + 1)

    Replace y by f^-1 (x).

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

    Done!

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  2. How did you go from here:

    x = y(4 - y)

    To here:

    Next:

    xy = 4 - y

    Shouldn't you divide rather than multiply?

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  3. Mike,

    After doing the question again, I realize that 4x - x^2 is not one-to-one. Hence, it has no inverse function.

    Sorry....The answer is: NO INVERSE FUNCTION HERE.

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