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Thread: Problem with solving function

  1. #1
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    Problem with solving function

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

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

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

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

    $\displaystyle f(5)=\vert 5\vert + 2 x^2 + x^4 = 5 +2(5)^2 + (5)^4 = 680$
    Last edited by bigwave; Dec 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
    $\displaystyle f(x^2+1)=\vert x\vert + 2 x^2 + x^4$

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

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

    combine like terms

    $\displaystyle x^4 + 3x^2 + 1$

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

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

    $\displaystyle f(5)=\vert 5\vert + 2 x^2 + x^4 = 5 +2(5)^2 + (5)^4 = 680$
    But why you didnt insert $\displaystyle x^2+1$ in to other $\displaystyle x$ 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; Dec 1st 2009 at 12:56 PM. Reason: wording
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