In this problem, we consider some functions that are based on the symmetries of the regular pentagon. b Let P = {a,b, c, d, e}, and let r : P → P be the function that rotates the pentagon clockwise by 72° (i.e., one fifth of a rotation). That is, r = {(a, b), (b, c), (c,d), (d, e), (e, a)}. Also, let fa : P → P be the function that reflects the pentagon along the line that passes through a and is perpendicular to cd. That is, fa= {(a, a), (b, e), (c, d), (d, c), (e, b)}. Now answer the following questions: (a) Is it true that fa or=rofa? Explain your answer. (b) Is it true that r−¹ = r (i.e., r is the inverse function of itself)? Explain your answer. (c) Is it true that f¹ = fa (i.e., fa is the inverse function of itself)? Explain your answer.

In this problem, we consider some functions that are based on the symmetries of the regular pentagon. b Let P = {a,b, c, d, e}, and let r : P → P be the function that rotates the pentagon clockwise by 72° (i.e., one fifth of a rotation). That is, r = {(a, b), (b, c), (c,d), (d, e), (e, a)}. Also, let fa : P → P be the function that reflects the pentagon along the line that passes through a and is perpendicular to cd. That is, fa= {(a, a), (b, e), (c, d), (d, c), (e, b)}. Now answer the following questions: (a) Is it true that fa or=rofa? Explain your answer. (b) Is it true that r−¹ = r (i.e., r is the inverse function of itself)? Explain your answer. (c) Is it true that f¹ = fa (i.e., fa is the inverse function of itself)? Explain your answer.

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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