Math

(f/g)(x)  =  f(x) / g(x)

f(x) =  -1/x

g(x)  =  sqrt(3x - 9)      <This differs from what was entered in the question: I'm assuming that this was meant.>

--->     f(x) / g(x)  =  [ -1/x ] / sqrt(3x - 9)     --->     f(x) / g(x)  =  -1 / [ x · sqrt(3x - 9) ]

Because of the 'x' term in the denominator, x cannot be zero.

Since square roots are defined only for positive numbers,  

           3x - 9  >= 0        <and can't be zero because it's in the denominator>

           3x - 9  >  0

                 3x  > 9

                   x  >  3

Therefore, the domain consists only for the real numbers:  x  >  3.

So will it look like this ---> (3,oo) or something?