Algebra and Trigonometry

(1) The Set A ={11k+8|k∈Z},B={4m|m∈Z}and C = {11(4n + 1) − 3|n ∈ Z} are given.

Prove that A ∩ B = C.

(2) Given f(x) = x3+2x2+x, find the domain, range, behaviour x2 −x−2

of f(x) and hence sketch the graph of the function.

(3) Determine the values of the real parameter m for which the set A = {X ∈ R|(m−1)x2 −(3m+4)x+12m+3 = 0} has:

(a) one element (b) two elements

(c) has no element.