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Problems: 1. Find the domain of g(x) = VX- - 9 In(4- x) . Explain your work and write out all your steps as well as your reasoning. Write short sentences to explain your reasoning. Questions 2-5: The below table lists the 20 most viewed videos on You Tube, as of September 6, 2021. No. Video name Uploader Views (billions) Upload date Baby Shark Dance Pinkfong Kids' Songs & Stories 9.27 June 17, 2016 Despacito Luis Fonsi 7.52 January 12, 2017 Johny Johny Yes Papa LooLoo Kids 5.68 October 8, 2016 Shape of You Ed Sheeran 5.45 January 30, 2017 See You Aga Wiz Khalifa 5.25 April 6, 2015 Bath Song Cocomelon - Nursery Rhymes 4.49 May 2, 2018 Learning Colors Miroshka TV 4.46 February 27, 2018 Masha and the Bear Get Movies 4.46 January 31, 2012 9 Uptown Funk Mark Ronson 1.28 November 19, 2014 10 Gangnam Style Psy 4.18 July 15, 2012 11 Phonics Song with Two Words ChuChu TV 1.14 March 6, 2014 12 Dame Tu Cosita El Chombo 3.57 April 5, 2018 13 Sugar Maroon 5 3.54 January 14, 2015 14 Sorry Justin Bieber 3.46 October 22, 2015 15 Roar Katy Perry 3.42 September 5, 2013 16 Counting Stars OneRepublic 3.38 May 31, 2013 Thinking Out Loud Ed Sheeran 3.31 October 7, 2014 18 Wheels on the Bus Cocomelon - Nursery Rhymes 3.24 May 24, 2018 19 Dark Horse Katy Perry 3.14 February 20, 2014 20 Faded Alan Walker 3.13 December 3, 2015 Table 1: source: https://en. wikipedia. org/wiki/List_of_most-viewed_YouTube_videos Consider the following relations, based on the table above. Note: In each case, the domain is in the table above (videos that are not in the table are not relevant). 2. Consider the relation Y where v is the video name, and Y'(v) is the Year the video was uploaded. (Note: Y(v) is the year, not the date, of upload.) (a) What is Y'(Gangnam Style)? (b) Is Y' a function? Explain why or why not. (c) Is Y invertible? Explain why or why not. 3. Now consider the relation V where u is the name of the uploader, and V(u) is the name of the Video. Is V a function? Explain why or why not. 4. Consider the relation N where v is the video name, and N(v) is its Number in the list (for example NV(Sorry) = 14). (a) Explain how we can tell that this is an invertible function. (Note: you must explain both why it is a function, and why it is invertible.) (b) What is N-17 Explain in words what NV- does, and state the domain and range of N-1. Give an example of evaluating N- (choose one example value, and evaluate NV- of that example). 5. Using the table, find an example of a relation that is a function but that is not invertible. Explain how you know that your relation has the right properties. (Your example must be new. You can not use an example that has already been used on this assignment.)