Sagot:
Ang domain ay #x in -oo, 2 uu 3, + oo #
Paliwanag:
#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)) #
Samakatuwid, # (3-x) / (2-x)> = 0 # at #x! = 0 #
Upang malutas ang hindi pagkakapantay-pantay na ito, ginagawa namin ang isang tsart ng pag-sign
#color (white) (aaaa) ## x ##color (white) (aaaaa) ## -oo ##color (white) (aaaaaa) ##2##color (white) (aaaaaaa) ##3##color (white) (aaaaaa) ## + oo #
#color (white) (aaaa) ## 2-x ##color (white) (aaaaa) ##+##color (white) (aaa) ## ##color (white) (aaa) ##-##color (white) (aaaaa) ##-#
#color (white) (aaaa) ## 3-x ##color (white) (aaaaa) ##+##color (white) (aaa) ## ##color (white) (aaa) ##+##color (white) (aaaaa) ##-#
#color (white) (aaaa) ##g (f (x)) ##color (white) (aaaa) ##+##color (white) (aaa) ## ##color (white) (aaa) ## O / ##color (white) (aaaaaa) ##+#
Samakatuwid, #g (f (x)> = 0) #, kailan #x in -oo, 2 uu 3, + oo #
Ang domain ay #D_g (f (x)) # ay #x in -oo, 2 uu 3, + oo #
