Question

fx=3x/x2+x+1(x>0)的值域

Answer 1

f(x)=3x/(x^2+x+1)=3x/[(x-1/2)^2+3/4]

x＞0时,f(x)＞0

令f(x)=3x/(x^2+x+1)=m

mx^2+(m-3)x+m=0

判别式=(m-3)^2-4m*m≥0

3m^2+6m-9≤0

(m+3)(m-1)≤0

-3≤m≤1,即：

-3≤f(x)≤1

又：f(x)＞0,所以：

0＜f(x)≤1

值域（0,1]