Let f : Z → Z be the function defined by putting f (x) = 2x/3 for each x ∈ Z. (a) Is f one-to-one? Prove your answer. (b) Is f onto? Prove your answer. (c) Is there a function g : Z −→ Z so that g ◦ f is one-to-one? Prove your answer. (d) Is there a function h : Z −→ Z so that f ◦ h is not onto Z? Prove your answer

Let f : Z → Z be the function defined by putting f (x) = 2x/3 for each x ∈ Z. (a) Is f one-to-one? Prove your answer. (b) Is f onto? Prove your answer. (c) Is there a function g : Z −→ Z so that g ◦ f is one-to-one? Prove your answer. (d) Is there a function h : Z −→ Z so that f ◦ h is not onto Z? Prove your answer

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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