函数y=(x2-x)/(x2-x+1)的值域

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函数y=(x2-x)/(x2-x+1)的值域函数y=(x2-x)/(x2-x+1)的值域函数y=(x2-x)/(x2-x+1)的值域去分母得:x^2(y-1)+x(1-y)+y=0y=1时,上式无解y

函数y=(x2-x)/(x2-x+1)的值域
函数y=(x2-x)/(x2-x+1)的值域

函数y=(x2-x)/(x2-x+1)的值域
去分母得:x^2(y-1)+x(1-y)+y=0
y=1时,上式无解
y=1时,为二次式,须有delta>=0
即 (1-y)^2-4y(y-1)>=0
(y-1)(3y+1)

y=(x^2-x)/(x^2-x+1)=(x^2-x+1-1)/(x^2-x+1)=1-1/(x^2-x+1)
x^2-x+1=(x-1/2)^2+3/4≥3/4
0<1/(x^2-x+1)≤4/3
1>1-1/(x^2-x+1)≥-1/3
值域[-1/3, 1)