Svar:
#S: x i -oo; 0 uu 1 + sqrt2; + oo #
Forklaring:
# 1 / x <= | x-2 | #
#D_f: x i RR ^ "*" #
til #X <0 #:
# 1 / x <= - (x-2) #
# 1> -x²-2x #
# -X + 2x + 1> 0 #
# (X + 1) ²> 0 #
#x i RR ^ "*" #
Men her har vi den betingelse, at #X <0 #, så:
# S_1: x i RR _ "-" ^ "*" #
Nu, hvis #x> 0 #:
# 1 / x <= x-2 #
# 1 <= -X 2x #
# -X 2x-1> = 0 #
#Δ=8#
# X_1 = (2 + sqrt8) / 2 = 1 + sqrt2 #
#cancel (x_2 = 1-sqrt2) # (#<0#)
Så # S_2: x i 1 + sqrt2; + oo #
Langt om længe # S = S_1uuS_2 #
#S: x i -oo; 0 uu 1 + sqrt2; + oo #
0 / her er vores svar!
