Ano ang domain ng sqrt ((x ^ 2-x-6) / (x-4)?

Sagot:

Ang domain ay #x sa -2,3 uu (4, oo) #

Paliwanag:

Ang mga kondisyon ay

# ((x ^ 2-x-6) / (x-4))> = 0 # at #x! = 4 #

Hayaan #f (x) = ((x ^ 2-x-6) / (x-4)) = ((x + 2) (x-3)) / (x-4) #

Maaari naming bumuo ng tsart ng pag-sign

#color (white) (aaaa) ## x ##color (white) (aaaaa) ## -oo ##color (white) (aaaa) ##-2##color (white) (aaaaaaaa) ##3##color (white) (aaaaaaa) ##4##color (white) (aaaaa) ## + oo #

#color (white) (aaaa) ## x + 2 ##color (white) (aaaaaa) ##-##color (white) (aa) ##0##color (white) (aaaa) ##+##color (white) (aaaaa) ##+##color (white) (aaaaa) ##+#

#color (white) (aaaa) ## x-3 ##color (white) (aaaaaa) ##-##color (white) (aaaaaaa) ##-##color (white) (aa) ##0##color (white) (aa) ##+##color (white) (aaaaa) ##+#

#color (white) (aaaa) ## x-4 ##color (white) (aaaaaa) ##-##color (white) (aaaaaaa) ##-##color (white) (aaaaa) ##-##color (white) (aa) ##||##color (white) (aa) ##+#

#color (white) (aaaa) ##f (x) ##color (white) (aaaaaaa) ##-##color (white) (aa) ##0##color (white) (aaaa) ##+##color (white) (aa) ##0##color (white) (aa) ##-##color (white) (aa) ##||##color (white) (aa) ##+#

Samakatuwid, #f (x)> = 0 # kailan #x sa -2,3 uu (4, oo) #

graph {sqrt ((x ^ 2-x-6) / (x-4)) -12.66, 19.38, -6.05, 9.99}