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Unknown composite function

  1. Feb 2, 2017 #1
    1. The problem statement, all variables and given/known data
    Find f(x) given that f ( f(x) - x2) = x2 - 5x + 3

    2. Relevant equations
    Not sure

    3. The attempt at a solution
    I tried assuming f(x) = ax + b and use composite function but end up wrong. Please give me idea to start

    Thanks
     
  2. jcsd
  3. Feb 2, 2017 #2

    SammyS

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    It seems reasonable to assume that f(x) is a polynomial.

    If you compose linear function and a quadratic you get a quadratic function.

    One way to do that is for f(x) to be linear, which is what you tried & you say doesn't work.

    Another way is for f(x) to be a quadratic such that f(x) - x2 is linear.

    Try that.
     
  4. Feb 3, 2017 #3
    Thank you very much
     
  5. Feb 3, 2017 #4

    haruspex

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    To turn Sammy's remarks into a general approach, suppose f is a polynomial degree n. What are the possible degrees of f(x)-x2? What, then, are the possible degrees of f(f(x)-x2)?
     
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