Q111 / 180 · KCET 2020 · Mathematics
The domain of the function defined by $f(x)=\cos ^{-1} \sqrt{x-1}$ is
- Correct answerA$[1,2]$
- B$[0,2]$
- C$[-1,1]$
- D$[0,1]$
Solution
We have, $f(x)=\cos ^{-1} \sqrt{x-1}$ $f(x)$ is defined when $\sqrt{x-1} \in[0,1]$
$\begin{array}{ll}
\therefore \quad & 0 \leq \sqrt{x-1} \leq 1 \\
& 0 \leq x-1 \leq 1 \\
& 1 \leq x \leq 2
\end{array}$
$\therefore$ Domain of $f(x)$ is $[1,2]$.
Hence, the correct answer is option: 'A'.