Hi, John;
Hugh is correct, one of the first restrictions is the one he pointed out. Now, let me add some guidance that I hope will help you a bit. When defining/checking domain, discontinuities, poles and, if applicable, undefined points must be found so you can set all conditions that define your domain. For each particular function you'll have a series of restrictions. I guess that you may find your way to get the answer yourself, just take some guidelines for this particular case:
1 - denominator different of zero, meaning:
1-ln(9-sqrrt(x^2-9)) =! 0 ,hence
ln(9-sqrt(x^2-9)) =! 1
9-sqrt(x^2-9) =! e (2.7183...)
sqrt(x^2-9) =! 9-e (now you isolate x... your turn!)
2 - because it is a ln operand:
9-sqrt(x^2-9) > 0 , hence:
sqrt(x^2-9) > 9
3 - sqrt parameter should be greater than zero as well:
x^2-9 > 0 , hence
x^2 > 9 and
|x| > 3
Can you put all of these conditions together in one only? If so, you'll have your domain.
(at least I hope this is correct; have someone found anythng wrong here, please add corrections)
Cheers.
Luiz (Brazil)