how to find the domain of (fofof)(x)
where f(x)=sqrt(x-1)
Book answer is [2,infinity).
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.