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The domain of the function $f(x) =\large\frac{\sin ^{-1} (x-3)}{\sqrt {9-x^2}}$ is

$\begin{array}{1 1}(A)\;[2,3] \\(B)\;[2,3) \\(C)\;[1,2] \\ (D)\;[1,2) \end{array}$

The domain of the function $f(x) =\large\frac{\sin ^{-1} (x-3)}{\sqrt {9-x^2}}$ is $[1,2)$