Resposta:
El domini és #x in -oo, 2 uu 3, + oo #
Explicació:
#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)) #
Per tant, # (3-x) / (2-x)> = 0 i #x! = 0 #
Per solucionar aquesta desigualtat, fem un gràfic de signes
#color (blanc) (aaaa) ## x ##color (blanc) (aaaaa) ## -o ##color (blanc) (aaaaaa) ##2##color (blanc) (aaaaaaa) ##3##color (blanc) (aaaaaa) ## + oo #
#color (blanc) (aaaa) ## 2-x ##color (blanc) (aaaaa) ##+##color (blanc) (aaa) ## ##color (blanc) (aaa) ##-##color (blanc) (aaaaa) ##-#
#color (blanc) (aaaa) ## 3-x ##color (blanc) (aaaaa) ##+##color (blanc) (aaa) ## ##color (blanc) (aaa) ##+##color (blanc) (aaaaa) ##-#
#color (blanc) (aaaa) ##g (f (x)) ##color (blanc) (aaaa) ##+##color (blanc) (aaa) ## ##color (blanc) (aaa) ## O / ##color (blanc) (aaaaaa) ##+#
Per tant, #g (f (x)> = 0), Quan #x in -oo, 2 uu 3, + oo #
El domini és #D_g (f (x)) # és #x in -oo, 2 uu 3, + oo #
