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Show this problem 85 gemignani 74 3 parts b c d e

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Unformatted text preview: ap mk : Z5→Z5, by the formula mk(x) = kx (mod 5). a) For which of the k ∈ {0, 1, 2, 3, 4} is mk a permutation of Z5? Show this. b) For which of the k ∈ {0, 1, 2, 3, 4} is mk ­1 = mk? Show this. The set Z6, the integers mod 6, can be represented by symbols {0, 1, 2, 3, 4, 5}. For each element k of Z6, define the multiplication map mk : Z6→Z6, by the formula mk(x) = kx (mod 6). c) For which of the k ∈ {0, 1, 2, 3, 4, 5} is mk a permutation of Z6? Show this. Problem 8 5: Gemignani, 7.4 #3, parts b, c, d, e Problem 8 6: Gemignani, 7.5 #1 Problem 8 7: Gemignani, 7.5 #3 Problem 8 8: Let the function f: R → R be defined by f(x) = (1+x)2. Let T be the interval [ ­1, 1]. (Recall that the interval [a,...
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