a. Define g: Z Z by the rule g(n) = 4n 5, for all integers n. (i) Is g one-to-one Prove
Chapter 7, Problem 11(choose chapter or problem)
a. Define g: \(\mathbf{Z} \rightarrow \mathbf{Z}\) by the rule g(n) = 4n − 5, for all integers n.
(i) Is g one-to-one? Prove or give a counterexample.
(ii) Is g onto? Prove or give a counterexample.
b. Define G: \(\mathbf{R} \rightarrow \mathbf{R}\) by the rule G(x) = 4x − 5 for all real numbers x. Is G onto? Prove or give a counterexample.
Text Transcription:
mathbf Z rightarrow mathbf Z
mathbf R rightarrow mathbf R
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