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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 37E: Use graphical differentiation to verify that ddxex=ex.
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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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