Hi, I need help with my calculus homework. Please briefly explain and answer these questions. Take your time, thank you.

1. Find the domain of g(x) = Vx2 - 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 2 Despacito Luis Fonsi 7.52 January 12, 2017 3 Johny Johny Yes Papa LooLoo Kids 5.68 October 8, 2016 Shape of You Ed Sheeran 5.45 January 30, 2017 CT AF See You Agai Wiz Khalifa 5.25 April 6, 2015 6 Bath Song Cocomelon - Nursery Rhymes 4.49 May 2, 2018 7 Learning Colors Miroshka TV 4.46 February 27, 2018 8 Masha and the Bear Get Movies 4.46 January 31, 2012 9 Uptown Funk Mark Ronson 4.28 November 19, 2014 10 Gangnam Style Psy 4.18 July 15, 2012 11 Phonics Song with Two Words ChuChu TV 4.14 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 17 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(1 point) Suppose that g is the function given by the graph below. Use the graph to ll in the blanks in the following sentences. As 3 gets closer and closer to (but stays less than) 1, 9(3) gets as close as we want to As a; gets closer and closer to (but stays greater than) 1, 9(3) gets as close as we want to As :12 gets closer and closer (but not equal) to 1, does 9(3) get as close as we want to a single value? If such a value exists, enter it. If no such value exists, enter DNE. at: 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). . 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. . 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. . Consider the relation N where v is the video name. and N(v) is its Number in the list (for example N(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'l? Explain in words what N'l does, and state the domain and range of N'l. Give an example of evaluating N'l (choose one example value, and evaluate N'1 of that example). . 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.) nd the following values for f'1 . (1 point) Use the given graph of the function f to ____-____.____|____-____4____|_________+____|.___ \f(1 point) Four functions are given below. Perform the indicated compositions to determine which functions are inverse to each other. Be sure to simplify the results. x) 2 4m + 15 9(32) i 15 Mm) = i Jim) l ,4; 5-2 + Oil : 319(3)) : 90%)) : Conclusion: fandg '2 v inverses. f(h(2=)) : h(f(&=)) : Conclusion: fand h ? v inverses. J'(9(w)) = 90(3)) = Conclusion: 9 and j 7 v inverses. (1 point) Suppose N 2 t) is the total number of inches of snow that fall in the rst t days of January. Which of the statements below best explains the meaning of the INVERSE function f'l? O A. The number of days it takes to accumulate N inches of snow O B. The number of inches of snow on the ground after t days 0 C. The number of inches of snow accumulated in t days 0 D. The days for which there are N inches of snow on the ground 0 E. None of the above (1 point) Suppose it?) = |$| '3\": Then f_1(a:) = ifac 2 0, and f1(a:) = ifa: g 0. Hint: Compute the inverse function separately in the two cases. It may also help to draw the graph of f. (1 point) Solve each equation for at: (A) Solve 8(3'2) : 3 for m. a: = (B) Solve In a: + 111(2': 2) : 3 for (B. m: (1 point) Find the solutions of the exponential equation 3235e\"+6=0. Enter your answer as a comma-separated list, and enter none if there are no solutions