domain notation for a function

I was helping a student with her homework, then I got confused.

here's the picture.
http://img205.imageshack.us/img205/9510/domainih5.jpg

Define the domain for a composite function  f ( f (x) )

if f (x) =  sqrt ( x^2 -1 )

then

f ( f (x) ) = sqrt [ ( sqrt(x^2 -1) )^2 - 1 ]

so,

(sqrt (x^2 - 1) )^2 - 1 >= 0

solving this, I get

x>= +/- sqrt(2)

This is where I got stuck.

I forgot how to do inequalities like this...

the domain obviously is...

-sqrt (2) >= x >= sqrt (2)

I just can't remember for the life of me what rule in inequality gives
that...