Final answer:
The student's question about finding the Z-transform contains typos and unrelated expressions, making it unclear. The Z-transform typically involves applying a summation definition, but the correct functional forms are needed to provide an accurate calculation.
Step-by-step explanation:
The student is seeking the Z-transform of three different functions: (1/2)⁽; Cos(3k); delta(k-m)+step(k)+delta(k-2). Unfortunately, the question contains several typos and unrelated expressions that do not pertain to the calculation of a Z-transform. The standard method to find the Z-transform involves applying the definition which typically has the form Z{f(k)} = ∞
∞
sum_{k=-∞}^{∞} f(k) z^{-k}. However, to provide a meaningful answer, I'll need the correct and complete functional forms for each of the three functions mentioned. Without this clarification, calculating the Z-transform is not feasible.