Try analysing the polynomial inside the root:
> or = 0
and see what intervals you come up with.
The domain of the function f(x) = square root -x^2+9x-8 cosists of one or more of the following intervals : (-infinity, A], [A,B] and [B, infinity) where A< B
For each internval, anwser YES or NO to where the interval is included in the solution.
(- infinity, A] :____
[B, infinity): _____