函数y=2x²-2x+3/x²-x+1的值域是

函数y=2x²-2x+3/x²-x+1的值域是

函数y=2x²-2x+3/x²-x+1的定义域为R
y=2x²-2x+3/x²-x+1=2x²-2x+2+1/x²-x+1=2（x²-x+1）+1/x²-x+1=2+1/x²-x+1
x²-x+1=（x-1/2）²+3/4∴x²-x+1≥3/4∴0＜1/x²-x+1≤4/3∴2＜2+1/x²-x+1≤10/3
∴值域为（2,10/3].

y=2x²-2x+3/x²-x+1=2+1/[(x-1/2)^2+3/4]<=2+4/3=10/3,值域是(2,10/3]