函數f(x)=(x²;+x+1)/(x²;+1)的值域是

函數f(x)=(x²;+x+1)/(x²;+1)的值域是

f(x)=(x^2+x+1)/(x^2+1)
令=(x^2+x+1)/(x^2+1)=t
x^2+x+1= t(x^2+1)
(t-1)x^2-x+(t-1)=0
判別式=(-1)^2-4(t-1)^2≥0
(t-1)^2≤1/4
-1/2≤t-1≤1/2
1/2≤t≤3/2
值域【1/2,3/2】