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"Functions" Review Assignment

*1.*What's a function?*2.*What's a domain?*3.*What's a range?*4.*Which of the following diagrams represent a function? Let \(X = { 1 , 2 , 3 , 4 }\) and \(Y = { a , b , c , d }\) .*5.*Give a recursive definition for the following function: \(f : \mathbb{N} \rightarrow \mathbb{N}\) gives the number of snails in your terrarium \(n\) years after you built it, assuming you started with 3 snails and the number of snails doubles each year.*6.*What is a surjective function?*7.*What is an injective function?*8.*When a function is both injective and surjective, it is called what?*9.*Consider the function \(g : Z \rightarrow Z\) defined by \(g ( n ) = n^2 + 1\). Find \(g ( 1 )\) and \(g ( { 1 } )\) . Then find \(g^{−1}( 1 )\), \(g^{−1} ( 2 )\) , and \(g^{−1} ( 3 )\).

Levin, O. (2018-12-31). Discrete Mathematics: An Open Introduction. . (Mar 3, 2023)

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