Let `E_(1)={x in R :x ne 1 and (x)/(x-1) gt 0} and E_(2)={x in E_(1):sin^(-1)(log_(e)((x)/(x-1))) " is real number"}`
(Here, the inverse trigonometric function `sin^(-1)x` assumes values in `[-(pi)/(2),(pi)/(2)]`.)
Let `f:E_(1) to R` be the function defined by `f(x)=log_(e)((x)/(x-1)) and g:E_(2) to R` be the function defined by `g(x)=sin^(-1)(log_(e)((x)/(x-1))) .`
The correct option is
A. `a to s, b to q, c to p, d to p`
B. `a to r, b to r, c to u, d to t`
C. `a to s, b to q, c to p, d to u`
D. `a to s, b to r, c to u, d to t`