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Math Help - function compositions

  1. #1
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    function compositions

    Here's the problem: Find sets A, B and C and functions f:A\longrightarrow B, g:B\longrightarrow C and h:B\longrightarrow C for which f\circ h=f\circ g but g\not=h.
    It doesn't even have to be real example functions, just a picture would be good. I just can't think of anything. Thank you!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sfitz View Post
    Here's the problem: Find sets A, B and C and functions f:A\longrightarrow B, g:B\longrightarrow C and h:B\longrightarrow C for which f\circ h=f\circ g but g\not=h.
    It doesn't even have to be real example functions, just a picture would be good. I just can't think of anything. Thank you!
    how about A = B = C = \mathbb{R}. with f(x) = x^2,~g(x) = x, \mbox{ and }h(x) = -x

    can you find another example?
    Last edited by Jhevon; February 27th 2008 at 12:48 AM.
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  3. #3
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    Oh my god, I am so sorry, I typed the problem wrong. I meant g\circ f and h\circ f! Can you still help? The part I typed was part a of the problem, and I'm stuck on part b. I'm really sorry.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sfitz View Post
    Oh my god, I am so sorry, I typed the problem wrong. I meant g\circ f and h\circ f! Can you still help? The part I typed was part a of the problem, and I'm stuck on part b. I'm really sorry.
    how about g(x) = x,~h(x) = f(x) = 1

    try to find another
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  5. #5
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    ok, I understand, f must not be onto for it to work, so that there are elements in B that are outside the image of f. thank you!
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sfitz View Post
    ok, I understand, f must not be onto for it to work, so that there are elements in B that are outside the image of f. thank you!
    can you prove that?

    just kidding... well, you can if you want to
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  7. #7
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    I did prove it! That was the other part of the question, but I couldn't prove it without being able to think of an example
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sfitz View Post
    I did prove it! That was the other part of the question, but I couldn't prove it without being able to think of an example
    oh, ok. that's fine then
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