12. a. Suppose a function F: X→Y is one-to-one but notonto. Is F-1 (the inverse relation for F) a functionExplain your answer.-b. Suppose a function F: X Y is onto but not one-to-one. Is F-1 (the inverse relation for F) a functionExplain your answer.

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Answered: 12. a. Suppose a function F: X→ Y is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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7. The following table gives Tinas height above the ground while riding a A Ferris wheel, in relation to the time she was riding it. Time (s) 20 40 60 80 100 120 140 160 180 200 220 240 Height (m) 5 10 10 10 a) Draw a graph of the relation, using time as the independent variable and height as the dependent variable. b) What is the domain? c) What is the range? d) Is this relation a function? Justify your answer. e) Another student sketched a graph, but used height as the independent variable. What does this graph look like? f) Is the relation in part e) a function? Justify your answer.
1. Which of the following statements is true? Explain your choice. (A) All functions are relations. (B) All relations are functions.
How does number 1 differ than a relation? Please explain how, thank you. My teacher wants me to implication the first one however I don’t understand it so please help me. Thank you.
Determine the domain and range of the relation shown to the right. If the relation is not a function, explain why. The domain is and the range is (Use a comma to separate answers as needed.) Is the given relation a function? If not, explain why. OA. No, the given relation is not a function because each element of the domain has a unique corresponding element of the range. OB. No, the given relation is not a function because each element of the domain does not have a unique corresponding element of the range. OC. Yes, the given relation is a function. 00 6
| Let A = {3, 4, 5}, and B = {−5, -3, -2, -1}. Define a relation R from A to B as follows: For all (x, y) = A × B, (x, y) = R means that x = 1 - y. (a) Write R as a list of ordered pairs. (b) Draw an arrow diagram for R. (c) Is R a function? Justify your answer.
How do you show the image of the union of S and T is equal to the union of the image of S and the image of T if f is a function from A to B and S And T are subsets of A?
4. す e McGraw-Hill Connect Math www-awu.connectmath.com/alekscgi/x/Isl.exe/1o_u-lgNslkr7j8P3jH-IQUdXJcbUh5AL... (E Determine if the relation defines y as a one-to-one function of x. 4- 3- 2- 1- O The relation does not define y as a one-to-one function of x. O The relation defines y as a one-to-one function of x. O2022 McGrav Type here to search 在。
4. How do you graph the inverse of a relation using the graph of the relation? Be sure to include the graph of the original and the graph of the inverse. Clearly indicate both.
Let f be the invertible linear transformation represented by the matrix -2 ^-(-²¹) A = 1). 4 4 Find, in terms of and y, the equation of the image f(C) of the unit circle C. The equation is
1) Use algebraic means to show that x2 + y2 = 8 is not a function. Explain your process. 2)Is there any value(s) of the domain of x2 + y2 = 8 that passes the vertical line test? If so,name the value(s) and state whether or not the existence of this value makes this relation afunction.
Which of the following relations is not a function? I. {(1,1), (1,2), (2, 3)} II. {(1,1), (1, 2), (0, 2)} III. {(1,2), (2,3), (3, 3)} (a) I (b) II (c) III (d) I and II (e) II and III
8. Consider what happens to a relation when the coordinates of all its ordered pairs are switched. a) Give an example of a function that is still a function when its coordinates are switched. b) Give an example of a function that is no longer a function when its coordinates are switched. c) Give an example of a relation that is not a function, but becomes a function when its coordinates are switched.

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12. a. Suppose a function F: X→ Y is one-to-one but not onto. Is F-1 (the inverse relation for F) a function Explain your answer. b. Suppose a function F: X Y is onto but not one-to- one. Is F-1 (the inverse relation for F) a function Explain your answer.