answer the following questions. n-5 n is 1. We have a function f: Z Z...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
answer the following questions. n-5 n is 1. We have a function f: Z → Z defined as f(n) = {n+3 if n is odd. Find whether the function is injective and surjective. What would be the inverse of this function? 2. Consider three sets A, B, and C each with three elements, and define a function 'f from set A to B and a function 'g' from set B to C with the mapping of the elements you specify. After defining 'f' and 'g', discuss the composition of functions fog and gof on the sets A, B, and C that you have defined. Can both fog and gof be defined for the sets you have considered? Are they equal? Provide proof to support your answer. 3. There are 5 students; Ani, Leon, Linh, Liam, and Abdul with scores in computer science as 75, 60, 85, 95, and 60 respectively. They are graded by the University as B, C, B+, A, and C respectively. Define the mappings from students to marks and marks to grades explicitly. What are the domains and ranges of the functions? Can you make a composite function out of this? If yes, make the composite function and find if the composition of functions is commutative. Explain the reason. 4. Explain the following concepts using relevant examples: sequence, recursive function, closed formula for the sequence, arithmetic sequence, and geometric sequence. Ensure that you do not take the same examples discussed in the textbooks and online resources. 5. i. The sequence 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 12, 12........ can be generated by a closed formula. Find the formula and the next four terms of the sequence. ii. Find the next three terms of the series, provide a closed formula and calculate the sum to the first n terms for the following series: 6+36+216+................. iii. Find the next three terms of the series, provide a closed formula, and calculate the sum to the first n terms for the following series: 21+24+27+.. answer the following questions. n-5 n is 1. We have a function f: Z → Z defined as f(n) = {n+3 if n is odd. Find whether the function is injective and surjective. What would be the inverse of this function? 2. Consider three sets A, B, and C each with three elements, and define a function 'f from set A to B and a function 'g' from set B to C with the mapping of the elements you specify. After defining 'f' and 'g', discuss the composition of functions fog and gof on the sets A, B, and C that you have defined. Can both fog and gof be defined for the sets you have considered? Are they equal? Provide proof to support your answer. 3. There are 5 students; Ani, Leon, Linh, Liam, and Abdul with scores in computer science as 75, 60, 85, 95, and 60 respectively. They are graded by the University as B, C, B+, A, and C respectively. Define the mappings from students to marks and marks to grades explicitly. What are the domains and ranges of the functions? Can you make a composite function out of this? If yes, make the composite function and find if the composition of functions is commutative. Explain the reason. 4. Explain the following concepts using relevant examples: sequence, recursive function, closed formula for the sequence, arithmetic sequence, and geometric sequence. Ensure that you do not take the same examples discussed in the textbooks and online resources. 5. i. The sequence 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 12, 12........ can be generated by a closed formula. Find the formula and the next four terms of the sequence. ii. Find the next three terms of the series, provide a closed formula and calculate the sum to the first n terms for the following series: 6+36+216+................. iii. Find the next three terms of the series, provide a closed formula, and calculate the sum to the first n terms for the following series: 21+24+27+..
Expert Answer:
Answer rating: 100% (QA)
1 Function f Z Z fn n 3 if n is odd fn n 5 if n is even Injective A function is injective or onetoone if each element of the domain maps to a distinct element in the codomain In this case the function ... View the full answer
Related Book For
Financial Accounting and Reporting
ISBN: 978-0273744443
14th Edition
Authors: Barry Elliott, Jamie Elliott
Posted Date:
Students also viewed these law questions
-
Statement of Advice 1 Prepare a tax return for an entity (Australian private company) (10 marks for technical and calculation accuracy and relevance and 10 marks for writing style; refer to marking...
-
The population of a certain colony of bacteria increases by 5% each hour. After 7 hours, what is the percent increase in the population over the initial population?
-
Go to the BEA website at www.bea.gov/newsreleases/international/intinv / intinvnewsrelease.htm and download annual data starting in 1976 on the United States' end-of-year international investment...
-
Multiply using the product rule. 3/25xy 39xy
-
Kellaway Ltd is considering installing a computer controlled production line to significantly reduce its manufacturing costs. The annual after-tax cost savings are expected to be \($230\) 000, and...
-
Define halo error. How can halo error inhibit selecting the best strategies to pursue?
-
Financial health, from an organizational standpoint, refers to the overall state of a company's financial well-being and its ability to effectively manage its financial resources to meet its...
-
Ashton and Melody Webb are a married couple in their mid-20s. Ashton has a good start as an electrical engineer and Melody works as a sales representative. Since their marriage four years ago, Ashton...
-
Asoccer player heads a 0.75 kg ball. The ball approaches the player's head at 3.5 m/s and leaves 4.9 m/s at a 90 degree angle to its incoming pathway. What is the magnitude of the impulse delivere to...
-
You learned that when red snapdragons are bred with white snapdragons, the offspring are pink snapdragonsan example of incomplete dominance. What happens when you breed a pink snapdragon with another...
-
From the point of view of natural selection, why is it important for an organism to survive?
-
True or False: If the real minimum attractive rate of return is 8%, inflation is 4%, the tax rate is 40%, and money can be borrowed at 12% annual compound interest, then the loan should be repaid...
-
Broad-spectrum antibiotics are effective against a wide variety of bacteria. Narrow-spectrum antibiotics are effective against only certain types of bacteria. Public health officials have suggested...
-
Listen to this, your friend says, reading from a newspaper article. Scientists believe that most genetic mutations have no effect on organisms, a small number have a disadvantageous effect, and an...
-
Consider a rocket nozzle as shown in the figure to the right. Because the gases coming from the combustion chamber are so hot and at high pressure, the rocket nozzle needs to be cooled, especially in...
-
This problem continues the Draper Consulting, Inc., situation from Problem 12-45 of Chapter 12. In October, Draper has the following transactions related to its common shares: Oct 1 Draper...
-
Constructive review of the regulators. Required: (a) Obtain a copy of the Financial Reporting Councils Annual Review. (b) Prepare a profile of the members of the ASB. (c) Comment on the strengths and...
-
Sweden acquired 100% of the equity shares of Oslo on 1 March 20X1 and gained control. At that date the balances on the reserves of Oslo were as follows: The Revaluation reserve Kr10 million Retained...
-
On 1 January 20X0 Hill plc purchased 70% of the ordinary shares of Valley plc for £1.3 million. The fair value of the non-controlling interest at that date was £0.5 million. At the date...
-
Show all the steps leading to the integral balance equation (18.6) in the text. Use the following boundary conditions and verify Eq. (18.7). (i) At \(y=0, T=T_{\mathrm{S}}\). (ii) At...
-
Consider the flat-plate heat transfer to be solved by the similarity approach. Show all the details leading to Eq. (18.15). What are the boundary conditions on \(\theta\) ? Extend your MATLAB code to...
-
For fluids with \(\operatorname{Pr} <1\) the velocity profile is assumed to be a cubic for \(y
Study smarter with the SolutionInn App