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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) ‡ (g°f)(x). Calculate f¹(y) and g-¹(y) for all y R. (b) Verify that (gof)−¹(y) = (ƒ−¹ og¯¹)(y) for all y ≤ R, by calculating both the sides.

(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) ‡ (g°f)(x). Calculate f¹(y) and g-¹(y) for all y R. (b) Verify that (gof)−¹(y) = (ƒ−¹ og¯¹)(y) for all y ≤ R, by calculating both the sides.

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 E R. - (b) Let x ER. Show that (fog)(x) ‡ (g°f)(x). Calculate f¹(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.
Transcribed Image Text:(6) Let f(x) = 2x – 1 for all x € R. Let g(x) = x 2 for all x E R. - (b) Let x ER. Show that (fog)(x) ‡ (g°f)(x). Calculate f¹(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.
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