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F(f(x))= (x^4)-4(x^2)+2, find f(x).

  1. Oct 13, 2013 #1
    1. The problem statement, all variables and given/known data
    http://postimg.org/image/48919pl1x/


    2. Relevant equations
    f(f(x))= (x^4)-4(x^2)+2,



    3. The attempt at a solution
    [f(x)]^2=
    (x^4)-4(x^2)+2=
    [(x-2)^2]-(4x^2)+2

    i cant seem to square root (x^4)-4(x^2)+2...
     
  2. jcsd
  3. Oct 13, 2013 #2
    The question states that f(x) is a polynomial. Use this.

    http://en.wikipedia.org/wiki/Polynomial
     
  4. Oct 13, 2013 #3
    ok,i tried this solution
    let f(x)=a(x^2)+bx+c
    (a(x^2)+bx+c)*(a(x^2)+bx+c) =(x^4)-4(x^2)+2

    comparing the coefficient of x^2
    2c+b^2=-4 ---eqn(2)
    comparing the coefficient of constant,
    i get a c value of sqrt2 and -sqrt2
    which i try to fit into eqn(2) but dosent work out..
     
  5. Oct 13, 2013 #4

    arildno

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    f(f(x)) must also be evaluated on the bf(x)+c terms!!
     
  6. Oct 13, 2013 #5

    Mark44

    Staff: Mentor

    The image link is broken.
    No one else pointed this out, so I will. f(f(x)) is not the same as [f(x)]2.
    That's not relevant here, since you are not being asked to solve for f(x) in the equation [f(x)]2 = ...

    What you're working with is a composite of f with itself -- (f o f)(x) --, not the square of f(x).
     
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