Find the values of x which the function `f(x)=sqrt(log_(1//2)((x-1)/(x+5))` is defined.

Find the values of x which the function `f(x)=sqrt(log_(1//2)((x-1)/(x

1.	Find the values of x which the function `f(x)=sqrt(log_(1//2)((x-1)/(x+5))` is defined.
Answer» Correct Answer - ` x in (1, infty)` `f(x)=sqrt(log_(1//2(x-1)/(x+5)))` It is defined if `log_(1//2).(x-1)/(x+5) ge 0` ` rArr 0 lt(x-1)/(x+5) le 1` When `(x-1)/(x+5) gt 0, x in (-infty, -5) uu(1, infty)` ...(i) When `(x-1)/(x+5) le 1` `rArr (x-1)/(x+5) - 1 le 0` `rArr (-6)/(x+5) le 0` ` rArr x gt - 5` ...(ii) From (i) and (ii), ` x in (1, infty)`.