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Math Help - inverse functions

  1. #1
    Junior Member
    Joined
    Oct 2009
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    39

    inverse functions

    Find the inverse of f(x)=x+[x].

    Let g(x) be the inverse of f(x). I keep getting

    g(x)={ x/2 if x is an integer
    g(x)={ x-([x]/2) if x is not an integer

    This works for g(f(x))=I(x)

    but when I try f(g(x)),

    f(g(x))={x if [x] is even and
    f(g(x))={x-(1/2) if [x] is odd

    Which is not the identity function (clearly)...

    Also, I cannot figure out how to find the inverse of
    h(x)=x/(1-(x^2)) for -1<x<1
    If y is the inverse of h(x), I get (x/y)-xy=1 which reminds me of a circle or hyperbola or something but I cant rearrange it to make a recognizable formula...
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  2. #2
    Senior Member
    Joined
    Feb 2010
    Posts
    422
    What does [x] mean? The floor function?

    As for (x/y)-xy=1, write it as xy^2+y-x=0 and use the quadratic equation for y.
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  3. #3
    Junior Member
    Joined
    Oct 2009
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    [quote=maddas;491650]What does [x] mean? The floor function?
    quote]
    yep, it means the floor function
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