Concept:For f(x) to be defined, the square root in the denominator must be real and non-zero, and the inverse sine term must be valid.Explanation:The denominator requires 9−x2>0.So, ∣x∣<3, which gives −3<x<3. (i)The numerator sin−1(x−3) requires −1≤x−3≤1.Adding 3, we get 2≤x≤4. (ii)Taking the intersection of (i) and (ii):2≤x<3.Hence, the domain is [2,3).Answer:B. [2,3)