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Math Help - Problem with solving function

  1. #1
    Junior Member
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    Problem with solving function

    I have problem solving function with definition
    f:[1,\infty)\rightarrow \mathbb{R}
    f(x^2+1)=\vert x\vert + 2 x^2 + x^4
    for these two
    f(5)\  and\  f(x)

    im very lost...
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  2. #2
    Super Member bigwave's Avatar
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    f(x^2+1)=\vert x\vert + 2 x^2 + x^4

     = \vert x^2+1\vert + 2 x^2 + x^4

    since x^2 will always be positive then
    x^2+1 + 2( x^2+1)^2 +( x^2+1)^4
    ---------------

    f(5)=\vert 5\vert + 2 x^2 + x^4  =  5 +2(5)^2 + (5)^4 = 680
    Last edited by bigwave; December 1st 2009 at 12:16 PM. Reason: equation correction
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  3. #3
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    Quote Originally Posted by bigwave View Post
    f(x^2+1)=\vert x\vert + 2 x^2 + x^4

     = \vert x^2+1\vert + 2 x^2 + x^4

    since x^2 will always be positive then
    x^2+1 + 2 x^2 + x^4

    combine like terms

     x^4 + 3x^2 + 1

    this will factor using the quadradic equation but may not need to do this

    ---------------

    f(5)=\vert 5\vert + 2 x^2 + x^4  =  5 +2(5)^2 + (5)^4 = 680
    But why you didnt insert x^2+1 in to other x es
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  4. #4
    Super Member bigwave's Avatar
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    you are correct
    sorry i missed that
    makes it more complicated....
    i corrected it in the first reply
    Last edited by bigwave; December 1st 2009 at 12:56 PM. Reason: wording
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