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Math Help - Functions

  1. #1
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    Functions

    How we prove in a function f that f(R)=R?
    By proving that is '1-1'?
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  2. #2
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    If f:\mathbb{R}\to\mathbb{R}, i.e., it is declared that the domain and the codomain of f are \mathbb{R}, then the claim that f(\mathbb{R})=\mathbb{R} means that f is surjective. On the other hand, the fact that f is 1-1 means that it is injective. These are different concepts; none of them implies the other. For example, for f(x)=x^3-x we have f(\mathbb{R})=\mathbb{R}, but f is not 1-1.
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  3. #3
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    thank you man
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