# Injective and Surjective

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• Apr 9th 2009, 07:47 AM
modi4help
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
• Apr 9th 2009, 08:04 AM
Plato
Quote:

Originally Posted by modi4help
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 \$\displaystyle \mathbb{N}=\{0,1,2,3, \cdots\} \$ then the a) part function is surjective. WHY?
Clearly \$\displaystyle f(11)=f(2) \$ so it is not injective. WHY?

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