given that f(x)=1/square root (x-5),g(x)=x-1 determine the domain and range of gf(x)

Answer 1

If by gf(x) you mean g(x)*f(x) = (x-1)/√(x-5) then
domain: x>= 5
range: y >= 4

If you mean g(f(x)) = f(x)-1 = 1/√(x-5) - 1 then
domain: x > 5
range: y > -1