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Math Help - one-to-one and/or onto?

  1. #1
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    one-to-one and/or onto?

    Define h: Z -> Z by h(x) = 7|x| 6

    a. Is h one-to-one? Explain.

    b. Is h onto? Explain.


    I'm having a hard time finding an explanation for this one. I think it is one-to-one, but not onto. Is this correct? An explanation would be appreciated
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  2. #2
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    Is it true that h(1) = h( - 1)? One-to-one??

    Is is possible that h(x)=-1? Onto??
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  3. #3
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    Hi, Plato. Thanks for the response. I guess I'm just confused by this.

    Quote Originally Posted by Plato View Post
    Is it true that h(1) = h( - 1)? One-to-one??
    Yes, I think so...but I really can't explain why

    Quote Originally Posted by Plato View Post
    Is is possible that h(x)=-1? Onto??
    I don't believe so...???

    I guess if someone can help me think through this to determine why or why not.
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  4. #4
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    Ok, I've been trying to think my way through this. This is what I think so far.

    it is one-to-one, but not onto since x and x map to same element |x|

    Am I on the right track?
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  5. #5
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by relyt View Post
    Ok, I've been trying to think my way through this. This is what I think so far.

    it is one-to-one, but not onto since x and x map to same element |x|

    Am I on the right track?
    Hi relyt,
    what is the definition of one-to-one and onto?
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  6. #6
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    A function f is one-to-one if and only if whenever f(x) = f(y), x = y

    A function f (from set A to B) is onto if and only for every y in B, there is at least one x in A such that f(x) = y

    Ok, so

    It is not one to one since h(-4) = h(4)

    and I don't believe it would be onto then either
    Last edited by relyt; March 17th 2009 at 09:08 PM.
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  7. #7
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    Quote Originally Posted by relyt View Post
    Define h: Z -> Z by h(x) = 7|x| 6

    a. Is h one-to-one? Explain.

    b. Is h onto? Explain.


    I'm having a hard time finding an explanation for this one. I think it is one-to-one, but not onto. Is this correct? An explanation would be appreciated
    not 1-1
    h(2)=h(-2)

    not onto
    \not \exists c \in \mathbb{Z} s.t. h(c)=-50
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