The domain of the function $\mathrm{f}(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^2}}$ is
The domain of the function $\mathrm{f}(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^2}}$ is
- $(2,3)$
- $[2,3)$
- $[2,3]$
- $(2,3]$
Solution
$\begin{aligned}
& \text {To define } \mathrm{f}(x), 9-x^2\gt0 \Rightarrow|x| \lt 3 \\
& \Rightarrow-3 \lt x \lt 3 \text {, }...(i) \\
& \text { and }-1 \leq(x-3) \leq 1 \\
& \Rightarrow 2 \leq x \leq 4 \text {...(ii) }
\end{aligned}$
From (i) and (ii), $2 \leq x \lt 3$ i.e., [2, 3).
Asked in: MHT CET 2024 (16 May Shift 2)
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