Svar:
Domenet er #x i -oo, 2 uu 3, + oo #
Forklaring:
#f (x) = (x-1) / (2-x) #
#G (x) = sqrt (x + 2) #
# (Gof) (x) = g (f (x)) #
# = G ((x-1) / (2-x)) #
# = Sqrt ((x-1) / (2-x) 2) #
# = Sqrt (((x-1) 2 (2-x)) / (2-x)) #
# = Sqrt ((x-1 + 4-2x) / (2-x)) #
# = Sqrt ((3-x) / (2-x)) #
Derfor, # (3-x) / (2-x)> = 0 # og # ganger! = 0 #
For å løse denne ulikheten, gjør vi et tegnskilt
#COLOR (hvit) (AAAA) ## X ##COLOR (hvit) (aaaaa) ## -Oo ##COLOR (hvit) (aaaaaa) ##2##COLOR (hvit) (aaaaaaa) ##3##COLOR (hvit) (aaaaaa) ## + Oo #
#COLOR (hvit) (AAAA) ## 2-x ##COLOR (hvit) (aaaaa) ##+##COLOR (hvit) (AAA) ## ##COLOR (hvit) (AAA) ##-##COLOR (hvit) (aaaaa) ##-#
#COLOR (hvit) (AAAA) ## 3-x ##COLOR (hvit) (aaaaa) ##+##COLOR (hvit) (AAA) ## ##COLOR (hvit) (AAA) ##+##COLOR (hvit) (aaaaa) ##-#
#COLOR (hvit) (AAAA) ##G (f (x)) ##COLOR (hvit) (AAAA) ##+##COLOR (hvit) (AAA) ## ##COLOR (hvit) (AAA) ## O / ##COLOR (hvit) (aaaaaa) ##+#
Derfor, #G (f (x)> = 0) #, når #x i -oo, 2 uu 3, + oo #
Domenet er #D_g (f (x)) # er #x i -oo, 2 uu 3, + oo #
