Domain of f(x)= ^ -1 x-1 is : - Vidyadip

Question

Domain of $f(x)=\sin ^{-1} \sqrt{x-1}$ is :

✓

Answer

(A)
$f(x)=\sin ^{-1} \sqrt{x-1}$ will be defined if$
\begin{array}{ll}
& x-1 \geq 0 \text { and }-1 \leq \sqrt{x-1} \leq 1 \\
\Rightarrow & x \geq 1 \text { and } 0 \leq \sqrt{x-1} \leq 1 \quad[\because \sqrt{x-1} \geq 0] \\
\Rightarrow & x \geq 1 \text { and } 1 \leq x \leq 2 \\
\Rightarrow & x \in[1,2]
\end{array}
$
So, domain of $f(x)$ is $[1,2]$
Hence correct option is (A)

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