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