Hoe los je x / (x-2)> = 0 op?

Antwoord:

De oplossing is #x in (-oo, 0 uu (2, + oo) #

Uitleg:

Laat #f (x) = x / (x-2) #

Bouw een tekenbord

#color (wit) (aaaa) ##X##color (wit) (aaaa) ## -Oo ##color (wit) (AAAAAAA) ##0##color (wit) (aaaaaaaa) ##2##color (wit) (aaaaaa) ## + Oo #

#color (wit) (aaaa) ##X##color (wit) (aaaaaaaa) ##-##color (wit) (aaaa) ##0##color (wit) (aaaa) ##+##color (wit) (AAAAA) ##+#

#color (wit) (aaaa) ## X-2 ##color (wit) (AAAAA) ##-##color (wit) (aaaa) ####kleur (wit) (AAAAA)##-##color (wit) (aa) ##||##color (wit) (aa) ##+#

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

daarom

#f (x)> = 0 # wanneer ##

grafiek {x / (x-2) -10, 10, -5, 5}

Antwoord:

# (-oo, 0 # U # (2, + oo) #

Uitleg:

#x / (x - 2) 0 #

#x / (x - 2) 0 ": is waar als" {("hetzij", x 0 en x - 2> 0), ("of", x 0 en x - 2 <0):} #

#x 0 en x - 2> 0 #

# x> 2 #

#x 0 en x - 2 <0 #

#x 0 #

Antwoord: #x 0 # OF # x> 2 #

In intervalnotatie: # (-oo, 0 # U # (2, + oo) #