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Math Help - Composition & Functoins

  1. #1
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    Composition & Functoins

    hey all, need help with a problem

    Question: Use composition to show that f(x) = (x + 3) / (x - 2) and g(x) = (2x - 3) / (x - 1) are inverse of each other.

    Any help would be greatly appreciated, thanks

    -Laconian
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  2. #2
    Senior Member
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    What means that f and g are inverse of each other?
    Just that \forall x \in Dom(g), f(g(x))=x and \forall x \in Dom(f), g(f(x))=x

    For example, let x \in \mathbb{R}-\{1\},

    f(g(x))
    =f(\frac{2x-3}{x-1})
    =\frac{\frac{2x-3}{x-1}+3}{\frac{2x-3}{x-1}-2}
    =\frac{2x-3+3(x-1)}{2x-3-2(x-1)}
    =\frac{5x-6}{-1} !!! that's not what we wanted!

    But if we change f(x)=\frac{x+3}{x-1} by f(x)=\frac{x-3}{x-1}, as you can see, that would work. Then try with gof.
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