a. Define F: Z Z by the rule F(n) = 2 3n, for all integers n. (i) Is F one-to-one Prove
Chapter 7, Problem 12(choose chapter or problem)
a. Define F: \(\mathbf{Z} \rightarrow \mathbf{Z}\) by the rule F(n) = 2 − 3n, for all integers n.
(i) Is F one-to-one? Prove or give a counterexample.
(ii) Is F onto? Prove or give a counterexample.
b. Define G: \(\mathbf{R} \rightarrow \mathbf{R}\) by the rule G(x) = 2 − 3x 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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