设集合P={x|x^2-x-2≥0},Q={y|y=1/2×x^2-1,x∈P}则P交Q=

Question

设集合P={x|x^2-x-2≥0},Q={y|y=1/2 ×x^2-1,x∈P} 则P交Q=

Answer 1

x^2-x-2=(x+1)(x-2)≥0
x≤-1,x≥2
y=1/2 ×x^2-1≥-1
所以P∩Q={a|a=-1,a≥2}