Question 712623
Some confusion about what you are really asking.

{{{g(x)= -sqrt((x+1)^2)}}}, find g(-6).

Yes this has a solution.   {{{-sqrt((-6+1)^2) = -sqrt((-5)^2)}}}
={{{-sqrt(25)}}}
={{{-(5)}}}
={{{-5}}}


If you really meant, {{{-(sqrt(-6+1))^2}}}, then it is a bit different.