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The domain of the function defined by $f(x)=\sin^{-1}\sqrt{x-1}$ is

$\begin{array}{1 1}(A)\quad[1,2] & (B)\quad[-1,1]\\(C)\quad[0,1] & (D)\quad \text{none\;of\;these} \end{array}$
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  • Domain of \( sin^{-1}x\) is [-1,1]\)
Ans (A) [1,2]
By taking \(\sqrt{x-1}\), in the place of x in the domain
\( \Rightarrow -1 \leq \sqrt{x-1} \leq 1\: and \: x-1 \geq 0\)
\( \Rightarrow x-1 \leq 1 \: or \: x \leq 2 \: and \: x \geq 1\)
\(\Rightarrow \:Domain\:is\:[1,2]\)


answered Feb 18, 2013 by thanvigandhi_1
edited Mar 16, 2013 by thanvigandhi_1
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