I need help with two math questions please? Domain

I have a math test this week so I have been going over my notes and practicing some problems but I have had problems solving these. Not only answers but an explanation is highly appreciated :)

1- Find the domain of:

√(3-x) + √(x^2-1)


√(3-x) / √(x^2-1)


√(√x)


Cubic root of 1 - √x


√ (cubic root of 1-x)


Also, how do I write the following domain in intercept form: "all real numbers except +1/9 and -1/9"

for:√(3-x) + √(x^2-1)
{x element R : x<=-1 or 1<=x<=3}

for:√(3-x) / √(x^2-1)
{x element R : x<-1 or 1
for:√(√x)
{x element R : x>=0} (all non-negative real numbers)
(assuming a function from reals to reals)

for:Cubic root of 1 - √x
{x element R : x>=0} (all non-negative real numbers)

for:√ (cubic root of 1-x)
{x element R : x<=1}

ha.