A function k whose domain is the set of positive integers is defined as k(1)=4 and k(n)=k(n-1)-2. Function k was evaluated for several numbers. Which of the following are true? Select each correct answer. (A) k(-1)=-4 (B) k(0)=-2 (C) k(2)=2 (D) k(3)=0 (E) k(6)=3

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Understand Function Definition: Understand the function definition and domain. The function k is defined for positive integers, with k(1)=4 and k(n)=k(n-1)-2 for n > 1. This means that for each step n, the function value decreases by 2 from its previous value.Evaluate Statement A: Evaluate the truth of statement A. Since the domain of k is the set of positive integers, k(-1) is not defined. Therefore, statement A is false.Evaluate Statement B: Evaluate the truth of statement B. Similarly, k(0) is not defined because 0 is not a positive integer. Therefore, statement B is false.Evaluate Statement C: Evaluate the truth of statement C. Using the definition of k, we calculate k(2) as follows: k(2) = k(2-1) - 2 k(2) = k(1) - 2 k(2) = 4 - 2 k(2) = 2 Therefore, statement C is true.Evaluate Statement D: Evaluate the truth of statement D. Using the definition of k, we calculate k(3) as follows: k(3) = k(3-1) - 2 k(3) = k(2) - 2 k(3) = 2 - 2 (from the previous step) k(3) = 0 Therefore, statement D is true.Evaluate Statement E: Evaluate the truth of statement E. Using the definition of k, we calculate k(6) as follows: k(6) = k(6-1) - 2 k(6) = k(5) - 2 We need to find k(5) first, which requires finding k(4): k(4) = k(4-1) - 2 k(4) = k(3) - 2 k(4) = 0 - 2 (from step 5) k(4) = -2 Now we find k(5): k(5) = k(5-1) - 2 k(5) = k(4) - 2 k(5) = -2 - 2 k(5) = -4 Finally, we find k(6): k(6) = k(5) - 2 k(6) = -4 - 2 k(6) = -6 Therefore, statement E is false.

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