函数y=arctan(x+1)/x的值域为(-π/2,-π/4],则x的取值范围

Question

函数y=arctan(x+1)/x的值域为(-π/2,-π/4],则x的取值范围

Answer 1

-π/2=arctan(x+1)/x
(x+1)/x->-∞
x->0-
arctan(x+1)/x=-π/4
(x+1)/x=-1
x+1=-x
x=-1/2
所以
x的取值范围：【-1/2,0)