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Math Help - proving three different functions

  1. #1
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    proving three different functions

    Let f, g, h be functions each with range of R, such that f(g(x)) = x and g(h(x)) = x. Prove that f = h.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: proving three different functions

    You need to prove f=h thus \forall x: f(x)=h(x).
    So start with f(x) and try to get h(x) using the given information.
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    Re: proving three different functions

    what information? i dont see very much information in this question
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    Re: proving three different functions

    Quote Originally Posted by zannagorfe View Post
    what information? i dont see very much information in this question
    \forall t we have f[t]=f[g(h(t))]=f(g[h(t)])=h(t).

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