Wednesday, 27 March 2019

discrete mathematics - Functions images and inverse images

The objective of this question is to find if the function is a bijective function or not and if it is a bijective find its images and inverse images.



$$ f:\mathbb{Z^2} \to \mathbb{Z}$$
$$ f(n,k) = n^2k $$



We have to find inverses of   $ f^{-1}(\{0\}) $,  $ f^{-1}(\mathbb{N}) $  and  $ f(\mathbb{Z} \times \{1\}) $



But I fail to understand the approach to this problem, I do understand that they need to have unique mappings and co-domains must be matched, but could anyone help me make it analogous to this situation?




questions such $$y = x^2 $$ is not bijective since they have multiple images and are not bijective. Their inverse will be a sqaure root with + and - and hence its an invalid case. Could someone please correct my approach?

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