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(6) Let f(x) = 2x – 1 for all x € R. Let g(x) = x - 2 for all x € R. Let x ER. Show that (fog)(x) ‡ (gof)(x). Calculate f-¹(y) and g¯¹(y) for all y € R. Verify that (go ƒ)−¹(y) = (ƒ−¹ o g¯¹)(y) for all y ≤ R, by calculating both the sides. (a) (b) (c)

(6) Let f(x) = 2x – 1 for all x € R. Let g(x) = x - 2 for all x € R. Let x ER. Show that (fog)(x) ‡ (gof)(x). Calculate f-¹(y) and g¯¹(y) for all y € R. Verify that (go ƒ)−¹(y) = (ƒ−¹ o g¯¹)(y) for all y ≤ R, by calculating both the sides. (a) (b) (c)

Advanced Engineering Mathematics
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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(6) Let f(x) = 2x − 1 for all x € R. Let g(x) = x − 2 for all x € R. Let x E R. Show that (ƒ o g)(x) ‡ (gºf)(x). Calculate f-¹(y) and g¯¹(y) for all y ≤ R. Verify that (gof)−¹(y) = (ƒ−¹ o g¯¹)(y) for all y € R, by calculating both the sides. (b) (c)
Transcribed Image Text:(6) Let f(x) = 2x − 1 for all x € R. Let g(x) = x − 2 for all x € R. Let x E R. Show that (ƒ o g)(x) ‡ (gºf)(x). Calculate f-¹(y) and g¯¹(y) for all y ≤ R. Verify that (gof)−¹(y) = (ƒ−¹ o g¯¹)(y) for all y € R, by calculating both the sides. (b) (c)
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