SOLUTION: Let f∶ Z×Z→Z×Z be defined as f(m,n)=(3m+7n,2m+5n). Is f a bijection, i.e., oneto-one and onto? If yes then give a formal proof, based on the definitions of
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-> SOLUTION: Let f∶ Z×Z→Z×Z be defined as f(m,n)=(3m+7n,2m+5n). Is f a bijection, i.e., oneto-one and onto? If yes then give a formal proof, based on the definitions of
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Question 1074818: Let f∶ Z×Z→Z×Z be defined as f(m,n)=(3m+7n,2m+5n). Is f a bijection, i.e., oneto-one and onto? If yes then give a formal proof, based on the definitions of one-to-one and onto, and derive a formula for f−1. If no then explain why not. Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website! No, the function is not one-to-one. =(,) =(,)
So if the function is one-to-one, implies that and .
Just looking at the first component,
Let's assume
Then,
So, and f is not one-to-one.
