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Math Help - About functions

  1. #1
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    About functions

    Hi. PLease can you say me:
    Can i to represent a function as:


    About functions-imag1.jpg
    Is this function injective and constant both? Why? Thank you
    Attached Thumbnails Attached Thumbnails About functions-imag1.jpg  
    Last edited by user; July 29th 2014 at 11:31 AM.
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  2. #2
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    Re: About functions

    I'm not sure I understand your question. Are you saying that f is a function from A to B, that A contains the single member "u", B contains the single member "8" (or possibly "g"?) and f(u)= 8? If so, it is both "injective" and "surjective". It cannot be a "constant" function since f(u) is not u.
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  3. #3
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    Re: About functions

    Quote Originally Posted by HallsofIvy View Post
    I'm not sure I understand your question. Are you saying that f is a function from A to B, that A contains the single member "u", B contains the single member "8" (or possibly "g"?) and f(u)= 8? If so, it is both "injective" and "surjective". It cannot be a "constant" function since f(u) is not u.
    The function f:\mathbb{R} \to \mathbb{R} defined by f(x) = 0 is a constant function, and f(x) \neq x. A constant function means that the output is constant over the entire domain. So, yes, the OP's function (if it only acts on a single point) is a constant function.
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  4. #4
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    Re: About functions

    Ah, yes, don't know why I said that. Thanks for catching that!
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