y=x/(x^2+2x+3)的值域
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y=x/(x^2+2x+3)的值域
y=x/(x^2+2x+3)的值域
y=x/(x^2+2x+3)的值域
y=x/(x^2+2x+3)
yx^2+2yx+3y=x
即yx^2+(2y-1)x+3y=0 (*)
函数值y应使得方程(*)有解
当y=0时,解得x=0
当y≠0时,(*)有解的条件为
Δ=(2y-1)^2-12y^2≥0
8y^2+4y-1≤0
==>
(-1-√3)/4≤y≤(-1+√3)/4且y≠0
∴函数的值域为
[(-1-√3)/4,(-1+√3)/4]