Find the domain of `f(x)=sqrt(((1-5^x)/(7^(-1)-7)))`

Explanation

`g(x)=((1-5^(x))/(7^(-x)-7))ge 0 " or " (5^(x)-1)/(7^(-x)-7) le 0`
Now, `5^(x)-1=0 " or " x=0 " and " 7^(x)-7=0 " or " x= -1`.
The sign scheme of g(x) is as follows:

Hence, from the sign scheme of `g(x), x in (-oo,-1) cup [0,oo)`.