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  4. The domain of the function f(x) = (sin-1(x-3)/√9-x2) is

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

AIEEEAIEEE 2004Inverse Trigonometric Functions

Solution:

$9 − x^2 > 0$ and $−1≤ x − 3 ≤ 1 ⇒ x ∈[2, 3)$