This is very basic but I'm having doubts about my understanding of mappings, onto, one-to-one etc and the textbook I'm using isn't very clear.(adsbygoogle = window.adsbygoogle || []).push({});

1. Let α,β and γ be mappings from Z to Z defined by

α(n) = 3n

β(n) = 4n²+1

γ(n) = 2 + cos (nπ/2) ...this is (n(pi)/2

Which of the 3 mappings are onto or one-to-one, and determine which subset is the co-domain of the mapping γ?

2.

3. My understanding is, taking α(n) for example, 0 maps to 0, 1 maps to 3, -1 maps to -3 etc, means that the mapping is one-to-one but not onto, because not all integers in the codomain are mapped to e.g. -2, 2. If we are told the mappings are from Z to Z, does that mean than all integers are included in each set?I'm probably not being very clear about this...apologies but I have scoured the net for a clear definition or suitable example but can't find anything. Any help would be appreciated.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Mappings problem

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