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Inverse of Polynomials

  1. Sep 12, 2011 #1
    1. The problem statement, all variables and given/known data

    Let f(x) = 2x^3 + 5x + 3
    Find the inverse at f^-1(x) = 1

    2. Relevant equations
    N/A


    3. The attempt at a solution

    The only way that I know how to solve inverses is by solving for X, then replacing it by Y. Then I supposed I would sub 1 into the inverted polynomial. However I'm not sure how to solve for X.
    My attempt:
    y - 3 = 2x^3 + 5x
    (y - 3)/x = x(2x^2 + 5)

    Then, hopelessness. Any info will be extremely helpful for my test this Friday. Thank you.
     
  2. jcsd
  3. Sep 12, 2011 #2

    dynamicsolo

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    Homework Helper

    Your statement is a bit unclear -- I'm interpreting you to say that you want to find x = f-1(1) , that is, what value of x gives f(x) = 1 ?

    I don't think they want you to solve the cubic equation [itex]2x^{3} + 5x + 3 = 1 [/itex] (unless they taught you how to do so in your course). This doesn't come out nicely at all...

    I'm wondering if they're asking that if you had the function y = f-1(x)*, what value of x would give y = 1 ? This is equivalent to asking what f(1) equals: the value of f(1) is the number that f-1(x) would "take back" to 1 .


    *whatever that is exactly -- it wouldn't be pretty; instead, we will work with what is called the "implicit function"
     
  4. Sep 17, 2011 #3
    buddy think again;
    the answer is f(1)....
     
  5. Sep 17, 2011 #4

    HallsofIvy

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    Yes, as both dynamicsolo and abhishek ghos are saying, you are completely misunderstanding the problem. The problem does NOT as you to find the inverse function, which would be extremely complex. It only asks you to find the single value [itex]f^{-1}(1)[/itex].

    Use the fact that if [itex]f(x)= y[/itex] then [itex]x= f^{-1}(y)[/itex].
     
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