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Math Help - Discrete maths about one to one

  1. #1
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    Question Discrete maths about one to one

    (a). Define the function f:
    <br />
\mathbb{R}^{2}\rightarrow\mathbb{R}^{2} \\<br />
    by f(x,y) = (x+2y, 3x+4y). Is f one-to-one?
    (Justify your answer)

    (b). Define the function g:
    <br />
\mathbb{R}\rightarrow\mathbb{R}^{2} \\<br />
    by g(x) = (x+1, x+2). Is g onto?
    (Justify your answer)

    thanks!


    My answer
    (a) Yes
    (b) i am not sure about this one

    How to justify these?
    Last edited by mr fantastic; August 20th 2009 at 01:09 AM.
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  2. #2
    Junior Member
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    Discrete maths

    (a). Define the function f:
    <br />
\mathbb{R}^{2}\rightarrow\mathbb{R}^{2} \\<br />
    by f(x,y) = (x+2y, 3x+4y). Is f one-to-one?
    (Justify your answer)

    (b). Define the function g:
    <br />
\mathbb{R}\rightarrow\mathbb{R}^{2} \\<br />
    by g(x) = (x+1, x+2). Is g onto?
    (Justify your answer)

    thanks!
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  3. #3
    ynj
    ynj is offline
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    Quote Originally Posted by quah13579 View Post
    (a). Define the function f:
    <br />
\mathbb{R}^{2}\rightarrow\mathbb{R}^{2} \\<br />
    by f(x,y) = (x+2y, 3x+4y). Is f one-to-one?
    (Justify your answer)

    (b). Define the function g:
    <br />
\mathbb{R}\rightarrow\mathbb{R}^{2} \\<br />
    by g(x) = (x+1, x+2). Is g onto?
    (Justify your answer)

    thanks!
    (a)yes
    (b)no
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  4. #4
    Super Member Gamma's Avatar
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    Dec 2008
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    Iowa City, IA
    Posts
    517
    a) the matrix representing this equation is invertible
    b) is the point (3,5) in the image of this function?
    ynj is correct
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