设集合A={y|y=x^2-2x+3,x属于R},B={y|y=-x^2+2x+10,x属于R},求A并B

设集合A={y|y=x^2-2x+3,x属于R},B={y|y=-x^2+2x+10,x属于R},求A并B
设集合A={y|y=x^2-2x+3,x属于R},B={y|y=-x^2+2x+10,x属于R},求A并B

设集合A={y|y=x^2-2x+3,x属于R},B={y|y=-x^2+2x+10,x属于R},求A并B
y=x^2-2x+3=(x-1)^2+2≥2
y=-x^2+2x+10=-(x-1)²+11≤11
∴A={y|y≥2} B={y|y≤11}
A∪B=R

y=x^2-2x+3
=(x-1)^2+2≥2
所以A={y|y≥2}
y=-x^2+2x+10
=-(X^2-2X)+10
=-(x-1)^2+11≤11
所以B={y|y≤11}
则A并B=R

A=﹛Y▕ Y≥2﹜B={Y▕ Y≥9}
A∪B=﹛Y▕ Y ≥9﹜