Wat is het domein van sqrt ((x ^ 2-x-6) / (x-4)?

Antwoord:

Het domein is #x in -2,3 uu (4, + oo) #

Uitleg:

De voorwaarden zijn

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

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

We kunnen de tekentabel bouwen

#color (wit) (aaaa) ##X##color (wit) (AAAAA) ## -Oo ##color (wit) (aaaa) ##-2##color (wit) (aaaaaaaa) ##3##color (wit) (AAAAAAA) ##4##color (wit) (AAAAA) ## + Oo #

#color (wit) (aaaa) ## X + 2 ##color (wit) (aaaaaa) ##-##color (wit) (aa) ##0##color (wit) (aaaa) ##+##color (wit) (AAAAA) ##+##color (wit) (AAAAA) ##+#

#color (wit) (aaaa) ## X-3 ##color (wit) (aaaaaa) ##-##color (wit) (AAAAAAA) ##-##color (wit) (aa) ##0##color (wit) (aa) ##+##color (wit) (AAAAA) ##+#

#color (wit) (aaaa) ## X-4 ##color (wit) (aaaaaa) ##-##color (wit) (AAAAAAA) ##-##color (wit) (AAAAA) ##-##color (wit) (aa) ##||##color (wit) (aa) ##+#

#color (wit) (aaaa) ##f (x) ##color (wit) (AAAAAAA) ##-##color (wit) (aa) ##0##color (wit) (aaaa) ##+##color (wit) (aa) ##0##color (wit) (aa) ##-##color (wit) (aa) ##||##color (wit) (aa) ##+#

daarom

#f (x)> = 0 # wanneer #x in -2,3 uu (4, + oo) #

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