Define a function f: Z→ Zx Z by f(x) = (2x + 5, x - 4). (a) Is fone-to-one? Prove or disprove. The function f ---Select--- one-to-one. Let a, b E Z, and suppose that f(a) = f(b). Then (2a + 5, a 4) =( eBook In order for the two ordered pairs to be equal, an item in one ordered pair must be equal the corresponding item in the other ordered pair, which is to say and 2a + 5 = a- In both cases, after simplifying it is clear that a = Therefore f ---Select--one-to-one. (b) Does f map Z onto Zx Z? Prove or disprove. The function f---Select--onto, because there is no x EZ such that f(x) = (2x + 5, x-4)= (-2,-2). Suppose to the contrary that there is such an x. So, 2x + 5 = cannot be because ---Select--- ✓. Therefore f-Select--onto. Solve for x and find that x must be . Th
Define a function f: Z→ Zx Z by f(x) = (2x + 5, x - 4). (a) Is fone-to-one? Prove or disprove. The function f ---Select--- one-to-one. Let a, b E Z, and suppose that f(a) = f(b). Then (2a + 5, a 4) =( eBook In order for the two ordered pairs to be equal, an item in one ordered pair must be equal the corresponding item in the other ordered pair, which is to say and 2a + 5 = a- In both cases, after simplifying it is clear that a = Therefore f ---Select--one-to-one. (b) Does f map Z onto Zx Z? Prove or disprove. The function f---Select--onto, because there is no x EZ such that f(x) = (2x + 5, x-4)= (-2,-2). Suppose to the contrary that there is such an x. So, 2x + 5 = cannot be because ---Select--- ✓. Therefore f-Select--onto. Solve for x and find that x must be . Th
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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all the options are: is or is not
Transcribed Image Text:Define a function f: Z→ Zx Z by f(x) = (2x + 5, x-4).
(a) Is f one-to-one? Prove or disprove.
The function f ---Select---
eBook
(2a + 5, a 4) = (
and
In order for the two ordered pairs to be equal, an item in one ordered pair must be equal to the corresponding item in the other ordered pair, which is to say
2a + 5 =
one-to-one. Let a, b € Z, and suppose that f(a) = f(b). Then
a-4 =
In both cases, after simplifying it is clear that a =
. Therefore f ---Select--- one-to-one.
(b) Does f map Z onto Z x Z? Prove or disprove.
The function f ---Select--- onto, because there is no x EZ such that f(x) = (2x + 5, x-4)= (-2,-2). Suppose to the contrary that there is such an x. So, 2x + 5 =
cannot be because ---Select--- ✓. Therefore f ---Select--- ✓onto.
Solve for x and find that x must be
This
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