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The domain is the set of all reals, since f(g(x))=x+1.

why is f(g(x)) = x+1 since the equation states f(g(x)) equals the square root of x-1

You plug in the square root of x-1 for x.

\[f(g(x))=(\sqrt{x-1})^{2}+2=(x-1)+2=x+1\]

oh great... this makes sense now. so what is the domain? hope I am asking the right question

x can be anything, so the domain is the set of all real numbers.

Thank you. you are a star!