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)