4. Let f : R+ x Z → R+ be the function defined by f (x,n) = x", where R+ is the set of positive real numbers and Z is the set of integers. (a) Is f one-to-one? Give a proof for your answer. (b) Is f onto? Give a proof for your answer. Determine f-1({1})

4. Let f : R+ x Z → R+ be the function defined by f (x,n) = x", where R+ is the set of positive real numbers and Z is the set of integers. (a) Is f one-to-one? Give a proof for your answer. (b) Is f onto? Give a proof for your answer. Determine f-1({1})

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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Question

4. Let f : R+ x Z → R+ be the function defined by f(x,n) = x", where R+ is the set of
positive real numbers and Z is the set of integers.
(a)
Is f one-to-one? Give a proof for your answer.
(b)
Is f onto? Give a proof for your answer.
(c)
Determine f-1({1}).

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