range and domain of a function

let f(x) = x^3 +x^2 -3x-3 and g(x) =1/(x+1)

(i) factorize f(x) completely and find the roots of f(x) = 0

(ii) find gf and its domain

(iii) let h(x) = x^2 -3. is gf = h? justify...

(iv) find the range of gf

my answer...

(i) by long division i got f(x) = (x+1) (x^2-3)

since f(x) = 0 , the roots are -1, -sqrt(3) and sqrt(3)

(ii) gf = 1/(x+1) x (x+1) (x^2-3) = (x^2-3). thus the domain is R\{-1}

(iii) h(x) does not equal to gf because domain of h(x) is R while domain for gf is R\{-1}

(iv) i dunno. how to get range of gf??

is my answer i to iii correct?? anyone justify.... (Nerd)