Question

函数y=cosx/(2cosx+1)的值域是

函数y=cosx/(2cosx+1)的值域是？

要详细过程。。。谢谢了。。。

Answer 1

令a=cosx
则-1<=a<=1
y=a/(2a+1)
=(a+0.5-0.5)/(2a+1)
=(a+0.5)/(2a+1)-0.5/(2a+1)
=1/2-(1/2)/(2a+1)

-1<=a<=1
所以-1<=2a+1<=3
所以1/(2a+1)<=-1,1/(2a+1)>=1/3
则-(1/2)/(2a+1)>=1/2,-(1/2)/(2a+1)<=-1/6
则(1/2)-(1/2)/(2a+1)>=1,(1/2)-(1/2)/(2a+1)<=1/3
所以值域是(-∞,1/3]∪[1,+∞)

Answer 2

（0 1／3］上下同除cosx，当cosx趋向0时，值趋向于零，但cosx=1时 值为1/3