Let E1={x∈R: x≠1 and x/x-1>0}
and E2={x∈E1 :sin-1(loge(x/x-1)) is a real number}
(Here, the inverse trigonometric function sin 1 x assumes values in [-π/2,π/2].)
Let f : E1 → R be the function defined by f (x)=loge(x/x-1)
and g : E2 → R be the function defined by g(x)=sin-1(loge(x/x-1)).
The correct option is :