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Thread: Compositum of the functions

  1. #1
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    Exclamation Compositum of the functions

    We are given $\displaystyle f(x) = \dfrac{3x -1}{x +1}$ and $\displaystyle g(x) = 2x + 1$. We need to find function $\displaystyle h(x)$, if this is true: $\displaystyle f(g(x)) = g(h(x))$. How can I find this function $\displaystyle h(x)$?

    I figure it out that $\displaystyle f(g(x)) = \dfrac{6x + 2}{2x + 2}$, but I don't know how it goes next step?
    Last edited by lebdim; Jul 18th 2018 at 11:38 AM. Reason: I was mistaken at Latex Code.
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  2. #2
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    Re: Compositum of the functions

    Step 1: calculate $f(g(x))$. Step 2: set $g(h(x))=f(g(x))$. Step 3: solve for $h(x)$

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  3. #3
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    Re: Compositum of the functions

    How can I solve for $\displaystyle h(x)$?
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  4. #4
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    Re: Compositum of the functions

    $$g(h(x)) = \dfrac{6x+2}{2x+2}$$

    $$2h(x)+1 = \dfrac{6x+2}{2x+2}$$

    $$h(x) = \dfrac{1}{2}\left(\dfrac{6x+2}{2x+2}-1\right) = \dfrac{x}{x+1}$$
    Thanks from topsquark
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  5. #5
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    Re: Compositum of the functions

    Ok, thanks for your help! Woow, why I couldn't figure it out at first place... :P Thank you again!
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