MHT CET · Maths · Functions
The domain of the function \(\mathrm{f}(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^2}}\) is
- A \((2,3)\)
- B \([2,3)\)
- C \([2,3]\)
- D \((2,3]\)
Answer & Solution
Correct Answer
(B) \([2,3)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& \text {To define } \mathrm{f}(x), 9-x^2\gt0 \Rightarrow|x| \lt 3 \\
& \Rightarrow-3 \lt x \lt 3 \text {, }...(i) \\
& \text { and }-1 \leq(x-3) \leq 1 \\
& \Rightarrow 2 \leq x \leq 4 \text {...(ii) }
\end{aligned}\)
From (i) and (ii), \(2 \leq x \lt 3\) i.e., [2, 3).
& \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).
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