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Math Help - Checking if a function is surjective

  1. #1
    iva
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    Checking if a function is surjective

    I have this function

    y = (2x+1)/(x-1) where x is a real number not = 1

    which i am trying to check if it is surjective.

    I solve it:

    x = (y+1)/(y-2)

    Am I correct in saying that this is not surjective due to the fact that it does not have the restriction y not = 2 ?

    Thank you
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Checking if a function is surjective

    Quote Originally Posted by iva View Post
    I have this function

    y = (2x+1)/(x-1) where x is a real number not = 1

    which i am trying to check if it is surjective.

    I solve it:

    x = (y+1)/(y-2)

    Am I correct in saying that this is not surjective due to the fact that it does not have the restriction y not = 2 ?

    Thank you
    The function is not surjective because there is no x such that y = 2.
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  3. #3
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    Re: Checking if a function is surjective

    the question depends on which range is specified......please defined function completely
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  4. #4
    iva
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    Re: Checking if a function is surjective

    Thanks, ok here is the full function (I was stuck at trying to determine the surjectivity and not really looking for an entire solution). Thanks for your reply alex but is this because due to the fact that y cannot be 2, and therefore the full spectrum of real numbers is not available as stated, is this why ut can't be surjective?

    Here is the whole function (I struggled to try find big curly braces to go around everything):


    g:= R->R

    g(x) = { (2x+1)/(x-1) if x not 1
    g(x) = { 2 if x = 1
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  5. #5
    MHF Contributor alexmahone's Avatar
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    Re: Checking if a function is surjective

    Quote Originally Posted by iva View Post
    g:= R->R

    g(x) = { (2x+1)/(x-1) if x not 1
    g(x) = { 2 if x = 1
    This function is surjective.
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  6. #6
    iva
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    Re: Checking if a function is surjective

    Thanks, but what about the fact that that y cannot be 2 when you solve the first equation?
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  7. #7
    MHF Contributor alexmahone's Avatar
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    Re: Checking if a function is surjective

    Quote Originally Posted by iva View Post
    Thanks, but what about the fact that that y cannot be 2 when you solve the first equation?
    Doesn't matter because the first equation by itself does not completely describe the function.

    The important thing is that there is an x (namely 1) such that g(x) = 2.
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  8. #8
    iva
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    Re: Checking if a function is surjective

    I get it now! thanks so much
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