Find the domain of `f(x)=sqrt((log)_(0. 4)((x-1)/(x+5)))`

Explanation

`f(x)=sqrt(log_(0.4)((x-1)/(x+5)))`
exists if
`log_(0.4)((x-1)/(x+5)) ge 0 " and " ((x-1)/(x+5)) gt 0`
or `(x-1)/(x+5) le (0.4)^(0) " and " (x-1)/(x+5) gt 0`
or `(x-1)/(x+5) le1 " and " (x-1)/(x+5) gt 0`
or `(x-1)/(x+5) -1 le 0 " and " (x-1)/(x+5) gt 0`
or `(-6)/(x+5) le 0 " and " (x-1)/(x+5) gt 0`
or `x+5 gt 0 " and " (x-1)/(x+5) gt 0`
or `x gt -5 " and " x-1 gt 0 " " ("As " x+5 gt 0)`
or `x gt -5 " and " x gt 1 `
Thus, the domain f(x) is `(1,oo).`