The domain of f(g(x)) is the intersection of the domain of f with the domain of g. Extending the concept to three functions, the domain of f(g(h(x)) is the intersection of the domain of f with the domain of g with the domain of h.

The domain of is all such that . This implies that .

The domain of is all such that and (from the domain of ). Let's solve the inequality in terms of .

The intersection of and is , so the domain of is .

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The domain of is all such that and (from the domain of ). Let's solve the inequality in terms of .

The intersection of and is , so the domain of is .

I believe the answer in your book is incorrect assuming I did not err.