(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+2×2+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.