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Math Help - Injective and Surjective

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    Injective and Surjective




    determine whether the following functions are injective and/or surjective. For each function and for each poperty. prove your claim.
    (a) f: N ---> N is the function defined by f(n) = the sum of digits of n.
    (b) g: N ---> R is the function defined by g(x) = x/(1+x^2).
    (c) h: N ---> N is the function defined by h(n) = l_ (n^2+3) _l
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  2. #2
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    Quote Originally Posted by modi4help View Post
    determine whether the following functions are injective and/or surjective. For each function and for each poperty. prove your claim.
    (a) f: N ---> N is the function defined by f(n) = the sum of digits of n.
    (b) g: N ---> R is the function defined by g(x) = x/(1+x^2).
    (c) h: N ---> N is the function defined by h(n) = l_ (n^2+3) _l
    If \mathbb{N}=\{0,1,2,3, \cdots\} then the a) part function is surjective. WHY?
    Clearly f(11)=f(2) so it is not injective. WHY?

    Now you show some effort on parts b) & c).
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