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Math Help - Inverse Function

  1. #1
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    Inverse Function

    P(c)=-c^2+110c-2400

    I need to find the inverse function.

    Here's what I have done:
    P=-c^2+110c-2400
    P+2400=-c^2+110c
    P+2400=-c(c-110)
    -P-2400=c(c-110)

    I know I need to solve for c, but I'm not sure what to do next...
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  2. #2
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    Re: Inverse Function

    Start with your first step. Solve for c via the quadratic formula (or factoring if it's possible).

    I don't think you'll end up with an inverse function though...P(c) is not bijective.
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  3. #3
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    Re: Inverse Function

    The two values I got for c were 30 and 80. P(c) represents the daily profit earned as related to the number of cases, c, produced and sold. I have to find a function that gives the number of cases based on the profit desired. Wouldn't that be the inverse function?
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  4. #4
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    Re: Inverse Function

    You need to subtract P from both sides first:
    0=-c^2+110c-2400-P
    Now you can do the quadratic equation with a=-1, b=110, and c=-2400-P (that's c in the quadratic equation, not c the number of cases).

    What richard1234 is saying is that when you write out the quadratic equation, you get two solutions (because of the + or -), and you can't have a function with two outputs for the same input. You need more information to figure out which is correct, + or -.

    Sometimes in problems like this, the "-" solution ends up being physically impossible - like the number of cases being negative. I don't think that happens in your problem, though.

    - Hollywood
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  5. #5
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    Re: Inverse Function

    Technically, since that function is not "one-to-one", it does not have an inverse. That's why you get the " \pm" when you solve using the quadratic formula.
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