4. Let f, g be the functions R →R given by{ if z < 5VI+4 if r > 55 – 3r if r <1f(r) =g(r) =5 – 2r – r² if r>1,For each of these functions, determine whether they are invertible and if so, find their inverses.

Answered: Image /qna-images/answer/b318920c-aeec-4cf4-ae26-f1244ffb78c4.jpg

Answered: 4. Let f, g be the functions R → R…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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8 5) Let g(t) = +2vt be a real-valued function. Evaluate each of the following: t a) g(4) b) g c) g(-4)
4. Does the function represented by the set {(1, 2), (2, 3), (3, 4), (4, 8), (5, 10)} represent an invertible function? If yes, list the corresponding set of z- and y-values for the inverse function. O Yes, the set represents an invertible function. The corresponding set of a- and y-values for the inverse function is {(2,1), (3, 2), (4, 3), (8, 4), (10, 5)}. O No, the set does not represent an invertible function. O Yes, the set represents an invertible function. The corresponding set of z- and y-values for the inverse function is{(2, –1), (3, –2), (4, –3), (8, –4), (10, -5)}. O Yes, the set represents an invertible function. The corresponding set of a- and y-values for the inverse function is{(-1, -2), (–2, –3), (-3, –4), (-4, –8), (–5, –10)}. 9 Type here to search
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A group of researchers found that people prefer YouTube videos that aren't too long, but not too short either. Suppose these researchers determined that the ratings people gave to a video could be approximated byR(t)=20t/t^2 + 100 where t is the length of the video in minutes and R(t) is its rating. What length of video (in minutes) will get the highest rating?
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4. Let f, g be the functions R → R given by 5- 3r if r< 1 1 5- 21 – 2² if r > 1, { if z< 5 VI+4 if r > 5 f(z) = { g(1) = For each of these functions, determine whether they are invertible and if so, find their inverses.