Question

1.y=cosx/(2cosx+1)求值域

怎么求啊

Answer 1

y=cosx/(2cosx+1)
cosx=2ycosx+y,
cosx=y/(1-2y)
因为|cosx|<=1,所以|y/(1-2y)|<=1
所以|y/(1-2y)|^2<=1
即y^2<=(1-2y)^2,3y^2-4y+1>=0,(3y-1)(y-1)>=0
所以y<=1/3或y>=1