求值域,如图3,4
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求值域,如图3,4
![](http://img.wesiedu.com/upload/1/06/106ab1c572ec20280cfa94b4340672c2.jpg)
![](http://img.wesiedu.com/upload/1/06/106ab1c572ec20280cfa94b4340672c2.jpg)
![求值域,如图3,4](/uploads/image/z/20199558-30-8.jpg?t=%E6%B1%82%E5%80%BC%E5%9F%9F%2C%E5%A6%82%E5%9B%BE3%2C4%26nbsp%3B)
(3)
y= 2+√(2x-x)² = 2 + √[1-(x-1)²]
根号下无负数,2x-x²=-x(x-2)≥0
定义域:0≤x≤2
-1≤x-1≤1
0≤(x-1)²≤1
0≤1-(x-1)²≤1
0≤√[1-(x-1)²]≤1
2≤2+√[1-(x-1)²]≤3
值域【2,3】
(4)
y=(2x²-2x+3)/(x²-x+1)
= [2(x²-x+1)+1]/(x²-x+1)
= 2 + 1/(x²-x+1)
= 2 + 1/[(x-1/2)²+3/4]
(x-1/2)²+3/4≥3/4
0< 1/[(x-1/2)²+3/4]≤4/3
2< 2+ 1/[(x-1/2)²+3/4]≤ 10/3
值域(2,10/3】
y= 2+√(2x-x)² = 2 + √[1-(x-1)²]
根号下无负数,2x-x²=-x(x-2)≥0
定义域:0≤x≤2
-1≤x-1≤1
0≤(x-1)²≤1
0≤1-(x-1)²≤1
0≤√[1-(x-1)²]≤1
2≤2+√[1-(x-1)²]≤3
值域【2,3】
(4)
y=(2x²-2x+3)/(x²-x+1)
= [2(x²-x+1)+1]/(x²-x+1)
= 2 + 1/(x²-x+1)
= 2 + 1/[(x-1/2)²+3/4]
(x-1/2)²+3/4≥3/4
0< 1/[(x-1/2)²+3/4]≤4/3
2< 2+ 1/[(x-1/2)²+3/4]≤ 10/3
值域(2,10/3】