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Math Help - Composition of Functions

  1. #1
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    Composition of Functions

    f(x) = 1 / (x^3+5)
    g(x) = cubed root of [(1-5x) / x]
    Find f(g(x))


    I understand how to set it up but I keep getting stuck on the algebra.
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Hi there, I get...

     f(g(x)) = \frac{1}{\left(\sqrt[3]{\frac{1-5x}{x}}\right)^3+5}

     f(g(x)) = \frac{1}{\frac{1-5x}{x}+5}

     f(g(x)) = \frac{1}{\frac{1}{x}- \frac{5x}{x}+5}

     f(g(x)) = \frac{1}{\frac{1}{x}- 5+5}

     f(g(x)) = \frac{1}{\frac{1}{x}}

     f(g(x)) = x

    which means g(x) is the inverse of f(x) ??
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  3. #3
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    Thanks a lot for your help
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