What Determines the Domain of f(g(x)) for Given Functions?

[Coco12]

Let's say f(x) = sqrt(x-1)
And g(x) =x^2

What is the domain of f(g(x))

Well the domain of g(x) is all real numbers and the equation for the new function is sqrt(x^2-1)

Am I right to say that the domain for f(g(x)) is x greater than or equal to 1 and less than and equal to -1??

 

[Mark44]

Let's say f(x) = sqrt(x-1)
And g(x) =x^2

What is the domain of f(g(x))

Well the domain of g(x) is all real numbers and the equation for the new function is sqrt(x^2-1)

Am I right to say that the domain for f(g(x)) is x greater than or equal to 1 and less than and equal to -1??

Yes. In a bit nicer form it is $\{x | x \leq -1 \cup x \geq 1\}$.