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Math Help - [SOLVED] inverse functions

  1. #1
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    [SOLVED] inverse functions

    so i'm really lost with inverses..
    can someone just explain to me how to do it?

    g(x)= 1-1/(x-1)
    and
    g^-1(x)= 1+1/(1-x)

    how do you prove that they are or are not inverses?
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  2. #2
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    Quote Originally Posted by lonejunior View Post
    so i'm really lost with inverses..
    can someone just explain to me how to do it?

    g(x)= 1-1/(x-1)
    and
    g^-1(x)= 1+1/(1-x)

    how do you prove that they are or are not inverses?
    I've lost track of how many times I've said this, but: by showing that the definition holds.

    The definition of "inverse function" is:
    g^{-1} is the inverse function to g(x) if and only if g^{-1}(g(x))= x and g(g^{-1}(x))= x.

    If g(x)= 1- 1/(x-1) and g^{-1}(x)= 1+ 1/(1- x), then [tex]g^{-1}(g(x))= g^{-1}(1- 1/(x-1))= 1+ 1/(1-[1-1/(x-1)]). Show that that is equal to x and the do it the other way.
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