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Questions about what is an onto function and what is not

  1. Jul 13, 2004 #1
    onto or not?

    Hello ^_^

    I just have a few questions regarding onto functions. I'm a student studying BS Math here in the Phils. Right now i have a subject concerning math logic, and before we study the subject proper, my professor is discussing the basics of relations an functions ^_^;;; So if this question is misplaced Im truly sorry ^^;;;

    In my previous quiz, there was a question that asked "State whether the given function is onto or not:

    Domain = [-4,4], f(x) = x^2
    Domain = [-1,1], f(x) = sin x

    My understanding of an onto function is that it is a function wherein all the members of the codomain of the function should be assigned to at least one value of x in the domain. I answered that "yes, f(x)=x^2 is an onto function" because all the values of x in the domain have a corresponding y, i.e., there is no undefined value for any value of x or y. The next question's answer was was the same. However, when I asked for clarifications on what were the correct answers, my professor said that these two functions were not onto. Can someone please tell me why?

    Thanx in advance ^_^
    Last edited: Jul 13, 2004
  2. jcsd
  3. Jul 13, 2004 #2


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    Check out this Wikipedia article. Based on what's in that article, I don't understand how you can answer that function either way because there is no co-domain specified. The answer is yes to the first question if and only if the co-domain is a subset of [0,16]. The answer to the second question is yes if and only if the co-domain is a subset of [sin(-1), sin(1)].
  4. Jul 15, 2004 #3
    Thanks for the clarifications ^_^
  5. Jul 30, 2004 #4
    The co-domain for the function in the first question cannot be a proper subset of [0,16] or you would not have a function. Where you said "is a subset of" should be replaced with "equals" for both questions.
  6. Jul 30, 2004 #5
    Yes I don't see how you can answer that question. The values that the function maps to must be specified in order for you to answer the question.
  7. Jul 30, 2004 #6


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    What makes you say this? It's definitely a function. Check out that wikipedia link for what an "onto function" is for clarification. I believe I understood it correctly.
  8. Jul 30, 2004 #7
    I don't think it has anything to do with the function being onto or not. Can you exhibit a proper subset S of [0, 16] such that f: [-4, 4] -> S, f(x) = x^2 is a function? Remember,

    So (for example) f: [-4, 4] -> [0, 4] won't work since then f(3) = 9 would be in [0, 4].
    Last edited: Jul 30, 2004
  9. Jul 30, 2004 #8


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    Muzza you're right.
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