(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.
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