Hva er domenet til sqrt ((x ^ 2-x-6) / (x-4)?

Svar:

Domenet er #x i -2,3 uu (4, + oo) #

Forklaring:

Betingelsene er

# ((X ^ 2-x-6) / (x-4))> = 0 # og # ganger! = 4 #

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

Vi kan bygge skiltet

#COLOR (hvit) (AAAA) ## X ##COLOR (hvit) (aaaaa) ## -Oo ##COLOR (hvit) (AAAA) ##-2##COLOR (hvit) (aaaaaaaa) ##3##COLOR (hvit) (aaaaaaa) ##4##COLOR (hvit) (aaaaa) ## + Oo #

#COLOR (hvit) (AAAA) ## x + 2 ##COLOR (hvit) (aaaaaa) ##-##COLOR (hvit) (aa) ##0##COLOR (hvit) (AAAA) ##+##COLOR (hvit) (aaaaa) ##+##COLOR (hvit) (aaaaa) ##+#

#COLOR (hvit) (AAAA) ## x-3 ##COLOR (hvit) (aaaaaa) ##-##COLOR (hvit) (aaaaaaa) ##-##COLOR (hvit) (aa) ##0##COLOR (hvit) (aa) ##+##COLOR (hvit) (aaaaa) ##+#

#COLOR (hvit) (AAAA) ## x-4 ##COLOR (hvit) (aaaaaa) ##-##COLOR (hvit) (aaaaaaa) ##-##COLOR (hvit) (aaaaa) ##-##COLOR (hvit) (aa) ##||##COLOR (hvit) (aa) ##+#

#COLOR (hvit) (AAAA) ##f (x) ##COLOR (hvit) (aaaaaaa) ##-##COLOR (hvit) (aa) ##0##COLOR (hvit) (AAAA) ##+##COLOR (hvit) (aa) ##0##COLOR (hvit) (aa) ##-##COLOR (hvit) (aa) ##||##COLOR (hvit) (aa) ##+#

Derfor, #f (x)> = 0 # når #x i -2,3 uu (4, + oo) #

graf {sqrt ((x ^ 2-x-6) / (x-4)) -12,66, 19,38, -6,05, 9,99}