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Math Help - a question about proofing surjective

  1. #1
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    a question about proofing surjective

    • let f :R{1,-1}-R and f(x)=x/x2-1.
    • I am trying to show that the function is surjective,but i have the following questions:
    • 1)why we need to divide the case into 2 parts (1):y:R\{0} and (2)y=0 before proving it is surjective.
    • 2)and for part(1),why we need to show x:R\{1,-1}. I.e. x isn't equal to +1/-1
    • 3)BTW,for the definition of surjective,i don't know the pricinple behind f(x)=y (or why we need to show f(x)=y) (for all yY,the exists xX s.t. y=f(x)


    It would be great if you could help me
    Last edited by sethplau; October 15th 2012 at 05:40 PM.
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  2. #2
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    Re: a question about proofing surjective

    Quote Originally Posted by sethplau View Post
    • let f :R{1,-1}-R
    • F(x)=x/x2-1.
    • I am trying to show that the function is surjective,but i have the following questions:
    • 1)why we need to divide the case into 2 parts (1):y:R\{0} and (2)y=0
    • 2)and for part(1),why we need to show x:R\{1,-1}. I.e. x isn't equal to +1/-1
    • 3)and for the definition of surjective,i don't know the pricinple behind f(x)=y (or why we need to show f(x)=y) (for all yY,the exists xX s.t. y=f(x)
    I am not really sure what you want done.
    Consider f: (-1,1)\to\mathbb{R} defined be f(x)=\frac{x}{x^2-1}.
    That is a continuous onto function.
    Are you asking to have the onto part proven?
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  3. #3
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    Re: a question about proofing surjective

    I want to know how to prove the function is surjective.
    Though I've seen the detailed solution which show that the proof should be divied into 2parts
    , i don't really know why it should be proved through 2parts~
    Last edited by sethplau; October 15th 2012 at 05:43 PM.
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