6. Let g be a function that is differentiable throughout an open inter- val containing the origin. Suppose g has the following properties: g(x) + g(y) 1 - g(x)g(y) in the domain of g. for all real numbers x, y, and x + y i. g(x + y) = ii. lim g(h) = 0 h→0° 8(h) iii. lim h→0 h a. Show that g(0) = 0. b. Show that g'(x) = 1 + [g(x)]?. c. Find g(x) by solving the differential equation in part (b).

6. Let g be a function that is differentiable throughout an open inter- val containing the origin. Suppose g has the following properties: g(x) + g(y) 1 - g(x)g(y) in the domain of g. for all real numbers x, y, and x + y i. g(x + y) = ii. lim g(h) = 0 h→0° 8(h) iii. lim h→0 h a. Show that g(0) = 0. b. Show that g'(x) = 1 + [g(x)]?. c. Find g(x) by solving the differential equation in part (b).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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