# Math Help - Injective and Surjective

1. ## 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

2. 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 $\mathbb{N}=\{0,1,2,3, \cdots\}$ 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).