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Q. Find gf(x) and a suitable domain and the corresponding range.

so [itex]gf(x) = \sqrt{x-3}[/itex], f(x) is first and the domain for f(x) is x belongs to ℝ, so the domain for g(x) will be x belongs to ℝ, so this function doesn't work?

the answer is the domain is x>=3 and the range is x>=0, which I understand how they got but watching videos online and they separate each function, i.e do f(x) first, and find the domain and range for that, then the range becomes the domain for g(x), now I don't understand which way is correct