The domain of the function f(x)=sin−1(x−3)9−x2 is

f(x)=sin−1(x−3)9−x2 is defined iff−1≤x−3≤1and9−x2>0⇒ 2≤x≤4andx2−32<0⇒ (x+3) (x−3)<0∴ x∈[2, 3)

The domain of the function f(x)=sin−1(x−3)9−x2 is

f(x)=sin−1(x−3)9−x2 is defined iff−1≤x−3≤1and9−x2>0⇒ 2≤x≤4andx2−32<0⇒ (x+3) (x−3)<0∴ x∈[2, 3)

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$T h e d o m a i n o f t h e f u n c t i o n f (x) = \frac{\sin^{- 1} (x - 3)}{\sqrt{9 - x^{2}}} i s$

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$[2, 3]$

$[2, 3)$

$[1, 2]$

$[1, 2)$

answer is B.

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Detailed Solution

$\begin{array}{l} f (x) = \frac{\sin^{- 1} (x - 3)}{\sqrt{9 - x^{2}}} i s d e f i n e d i f f \\ - 1 \leq x - 3 \leq 1 a n d 9 - x^{2} > 0 \\ \Rightarrow 2 \leq x \leq 4 a n d x^{2} - 3^{2} < 0 \\ \Rightarrow (x + 3) (x - 3) < 0 \\ ∴ x \in [2, 3) \end{array}$