The function h: Z12 → Z18 is defined by the formula h([a]) = [3a — 5].(a) Verify that the function h is well-defined, that is, show that if a, b € Z are such that [a] = [b]in Z12 then [3a - 5] = [3b – 5] in Z18.

We are dealing with a function h:Z12→Z18 defined by h([a])=[3a−5].This function operates between…

Answered: The function h: Z12 → Z18 is defined…

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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9A
[D] Consider the function F: {1,5, 8} × {6, 10} → {0, 1, 2, 3, 4, 5} defined as follows: F: (a, b) → (4a + b)mod 6 (D.1) Fill in the ordered pairs in the diagram below to indicate the elements in the domain of F. Then draw in arrows to complete the diagram so that it correspondes to the function. ( • 0 • 1 • 2 • 3 • 4 • 5 (D.2) What is the range of F? (D.3) What is the co-domain of F? 3/5 (D.4) What is the preimage (inverse image) of 3? (D.5) What is the preimage (inverse image) of 0? (D.6) Is F one-to-one? If not provide a counterexample. (D.7) Is F onto? If not provide a counterexample.
For each of the following parts, write an equation based on the description and then solve the equation. Be sure to define a variable to represent the value of the unknown number before writing each equation. a. Some number is equal to one-fourth of the sum of 55.3, 108.5, and 138. What is the number? 13.825 Preview b. 325% of some number is 59.2. What is the number? 19.24 Preview
[F] { "I started my farm with one chick and now I am a billionaire!"} Mr Tumbo's wealth (in Kenyan shillings) is governed by the function f(x) = 10 + 2xe2. Find the corresponding values of f(x) for: a = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and use these to draw a forward difference table. From your table: Af3 A² fa A³ f3 Af9
Choose correct answer on each problem
The Domain of f x) is [3, 00) and range of f(x) is [2,3], then Select one: O a. domain of f(x) is [3, 00) and range of f(x) is [2, 3|] O b. domain of f(x) is [2, 3] and range of f(x) is (3, 00) O c. domain of f(x) is [2, 3] and range of f(x) is [2, 3] O d. domain of f(x) is [3, 00) and range of f(x) is [3, 00)

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The function h: Z12 → Z18 is defined the formula h([a]) = [3a - 5]. (a) Verify that the function h is well-defined, that is, show that if a, b € Z are such that [a] = [b] in Z12 then [3a - 5] = [3b - 5] in Z18.