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答:
1<=x<=2,1/2<=1/x<=1
y=(2x^2+4x+1)/x^2
y=2+4/x+(1/x)^2
y=(1/x +2)^2 -2
因为:5/2<=1/x + 2<=3
所以:25/4<=(1/x +2)^2<=9
所以:25/4 -2<=y<=9-2
所以:17/4<=y<=7
所以:值域为[17/4,7]
1<=x<=2,1/2<=1/x<=1
y=(2x^2+4x+1)/x^2
y=2+4/x+(1/x)^2
y=(1/x +2)^2 -2
因为:5/2<=1/x + 2<=3
所以:25/4<=(1/x +2)^2<=9
所以:25/4 -2<=y<=9-2
所以:17/4<=y<=7
所以:值域为[17/4,7]
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