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For each of the following functions, determine if the function is injective, whether it is surjetive, or whether it is bijective. If any propertty fails to hold, give a brief but explicit explanation why. If it does hold, you do not need to explain why. (Tip: Represent their inputs and outputs as a table) Also, note that these are the same functions as in 04 above. 1. f: Z5 → Z5 given by f(x) = (2x) % 5 2. g: Z6Z6 with g(x) = (2x) % 6

For each of the following functions, determine if the function is injective, whether it is surjetive, or whether it is bijective. If any propertty fails to hold, give a brief but explicit explanation why. If it does hold, you do not need to explain why. (Tip: Represent their inputs and outputs as a table) Also, note that these are the same functions as in 04 above. 1. f: Z5 → Z5 given by f(x) = (2x) % 5 2. g: Z6Z6 with g(x) = (2x) % 6

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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Learning Target 05: I can determine whether a function is injective. I can determine whether a function is surjective. If a function is bijective, I can find the inverse function. For each of the following functions, determine if the function is injective, whether it is surjetive, or whether it is bijective. If any propertty fails to hold, give a brief but explicit explanation why. If it does hold, you do not need to explain why. (Tip: Represent their inputs and outputs as a table) Also, note that these are the same functions as in 04 above. 1. f: Z5 → Z5 given by f(x) = (2x) % 5 2. g: Z6 → Z6 with g(x) = (2x) % 6
Transcribed Image Text:Learning Target 05: I can determine whether a function is injective. I can determine whether a function is surjective. If a function is bijective, I can find the inverse function. For each of the following functions, determine if the function is injective, whether it is surjetive, or whether it is bijective. If any propertty fails to hold, give a brief but explicit explanation why. If it does hold, you do not need to explain why. (Tip: Represent their inputs and outputs as a table) Also, note that these are the same functions as in 04 above. 1. f: Z5 → Z5 given by f(x) = (2x) % 5 2. g: Z6 → Z6 with g(x) = (2x) % 6
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