et r and y be real variables related by the equation r = y?.(a) Does this relationship represent y as a function of r? Justify your answer.(b) Suppose we restrict y 2 0. With this restriction, does this relationship represent y as a function of r?Explain why or why not.(c) Is there any way to restrict both r and y to make this relationship represent y as a one-to-one functionof x? If so, what is the restriction? If not, explain why.

We will find the answers to all the parts as following.

Answered: et a and y be real variables related by…

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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SIdes). r radius Areas = nr h height Area = h(2xr) Circumference 2ar Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r, so we can write that as A (r) = 2 rr² + 12 ar. What is the domain of A (r)? In other words, for which values of r is A (r) defined? Part b: Continue to assume that the height of your cylinder is 6 inches. Write the radius r as a function of A. This is the inverse function to A (r), i.e., to turn A as a function of r into r as a function of A r(A) = Hints: • To calculate an inverse function, you need to solve for r. Here, you would start with A = 2 Tr2 + 12 Tr. This equation is the same as 2 rr2 + 12 rr - A 0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula. You will want to keep A as a variable when you plug the values into the quadratic formula. 3 п+1 r+1 • If you want to type in in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the…
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