odpoveď:
Doména je #x in -oo, 2 uu 3, + oo #
vysvetlenie:
# 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)) #
Z tohto dôvodu
# (3-x) / (2-x)> = 0 # a túto chvíľu # násobok! = 0 #
Na vyriešenie tejto nerovnosti robíme tabuľku znakov
#COLOR (biely) (AAAA) ##X##COLOR (biely) (aaaaa) ## # -OO#COLOR (biely) (aaaaaa) ##2##COLOR (biely) (aaaaaaa) ##3##COLOR (biely) (aaaaaa) ## + Oo #
#COLOR (biely) (AAAA) ## 2-x ##COLOR (biely) (aaaaa) ##+##COLOR (biely) (aaa) ## ##COLOR (biely) (aaa) ##-##COLOR (biely) (aaaaa) ##-#
#COLOR (biely) (AAAA) ## 3-x ##COLOR (biely) (aaaaa) ##+##COLOR (biely) (aaa) ## ##COLOR (biely) (aaa) ##+##COLOR (biely) (aaaaa) ##-#
#COLOR (biely) (AAAA) ##G (f (x)) ##COLOR (biely) (AAAA) ##+##COLOR (biely) (aaa) ## ##COLOR (biely) (aaa) ## O / ##COLOR (biely) (aaaaaa) ##+#
Z tohto dôvodu
#G (f (x)> = 0) #, kedy #x in -oo, 2 uu 3, + oo #
Doména je #D_g (f (x)) # je #x in -oo, 2 uu 3, + oo #
