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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
Domain of $f(x)=\sin ^{-1} \sqrt{x-1}$ is :
  • ✓
    $[1,2]$
  • B
    $[-1,1]$
  • C
    $[0,1]$
  • D
    None of these
✓

Answer

Correct option: A.
$[1,2]$
(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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