Let g be a function that is differentiable throughout an open interval containing the origin. Suppose g has the following properties:

i.

ii.

iii.

a. Show that g(0) = 0.

b. Show that g′(x) = 1 + [g(x)]².

c. Find g(x) by solving the differential equation in part (b).

Transcribed Image Text:

g(x) + g(y) 1 - g(x)g(y) x + y in the domain of g. g(x + y) = for all real numbers x, y, and