Consider the following functions: f : R → Z g: Z → Z x Z f(r) = [x] +1 9(m) %3 (Зт — 1, т+1) Recall: [:1: R → Z denotes the ceiling function, namely [r] = min{m € Z : m 2 a}. Which three of the following statements are true? Select the three correct responses: A. f is surjective. B. ƒ is injective. C. f is a bijection. D. g is surjective. E. g is injective. F. g is invertible. G. The domain of the composition gof is Z. H. The codomain of the composition go f is Z × Z. I. The composition g o f is invertible.

Consider the following functions: f : R → Z g: Z → Z x Z f(r) = [x] +1 9(m) %3 (Зт — 1, т+1) Recall: [:1: R → Z denotes the ceiling function, namely [r] = min{m € Z : m 2 a}. Which three of the following statements are true? Select the three correct responses: A. f is surjective. B. ƒ is injective. C. f is a bijection. D. g is surjective. E. g is injective. F. g is invertible. G. The domain of the composition gof is Z. H. The codomain of the composition go f is Z × Z. I. The composition g o f is invertible.

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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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Consider the following functions:
g: Z- Z x Z
g(m) = (3m – 1, m+1)
f: R → Z
f(x) = [x] +1
Recall: [1: R → Z denotes the ceiling function, namely [æ] = min{m € Z :m > x}.
Which three of the following statements are true?
Select the three correct responses:
A. f is surjective.
B. ƒ is injective.
C. f is a bijection.
D. g is surjective.
E. g is injective.
F. g is invertible.
G. The domain of the composition gof is Z.
H. The codomain of the composition gof is Z x Z.
I. The composition gof is invertible.

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