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Consider the function f : {0, 1, 2,3, 4} → {0, 1, 2, 3, 4} defined by the formula f (x) = (x + 2) % 5 %3D

Consider the function f : {0, 1, 2,3, 4} → {0, 1, 2, 3, 4} defined by the formula f (x) = (x + 2) % 5 %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Consider the function f : {0, 1, 2, 3, 4} → {0, 1, 2, 3, 4} defined by the formula f (x) = (x + 2) %5 For each n e N, define f" : {0,1, 2, 3, 4} → {0, 1, 2, 3, 4} by the rule f"(x) = ƒ o ƒ o ...f(x) n times Which of the following statements is TRUE? (a) f³(x) = x for all a € {0,1,2, 3, 4}. (b) There exists x € {0, 1, 2, 3, 4} such that f10 (x) # x. (c) f²(0) = f³(1). (d) The domain of f is not equal to the codomain of f, so fn is not a function unless n = 1. Select one alternative: (c) (b) O (d) (a)
Transcribed Image Text:6. Consider the function f : {0, 1, 2, 3, 4} → {0, 1, 2, 3, 4} defined by the formula f (x) = (x + 2) %5 For each n e N, define f" : {0,1, 2, 3, 4} → {0, 1, 2, 3, 4} by the rule f"(x) = ƒ o ƒ o ...f(x) n times Which of the following statements is TRUE? (a) f³(x) = x for all a € {0,1,2, 3, 4}. (b) There exists x € {0, 1, 2, 3, 4} such that f10 (x) # x. (c) f²(0) = f³(1). (d) The domain of f is not equal to the codomain of f, so fn is not a function unless n = 1. Select one alternative: (c) (b) O (d) (a)
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