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Math Help - Define function

  1. #1
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    Define function

    Hi everyone.
    I've got a one task to do i need to show if the function g: R -> R^2 by g(x) = (x+1, x+2) is g onto?

    I think is not but i do not really know how to show this understanding.
    I'll be appreciate for any help.

    Regards
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  2. #2
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    Quote Originally Posted by Snowboarder View Post
    Hi everyone.
    I've got a one task to do i need to show if the function g: R -> R^2 by g(x) = (x+1, x+2) is g onto?
    What number would map to (0,0)?
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  3. #3
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    yes than it's not but how can i proof that mathematicly?
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  4. #4
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    Quote Originally Posted by Snowboarder View Post
    yes than it's not but how can i proof that mathematicly?
    There is nothing to prove.
    If g(x)=(0,0) then x+1=0~\&~x+2=0.
    What is wrong with that?
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  5. #5
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    ok if you see the diagram you may better understand. the domain is a line. the codomain is a plain and the range is a straight line in that plane. now is that range line the same as full plane ?? how can that be ... this is a good way of illuminating things. keep track of pictures.
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  6. #6
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    Simply assume that there exists x \in {R} such that g(x) = (0,0). This gives us:

    (I) x+1 = 0
    (II) x+2 = 0

    \Rightarrow x+1 = x+2 \Rightarrow 1 = 2 \Rightarrow contradiction.

    So there is no x \in {R} such that g(x) = (0,0) and thus g is not onto
    Last edited by Defunkt; August 24th 2009 at 06:43 AM. Reason: Typo
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