KCET · Maths · Functions
The domain of the function defined by \(f(x)=\cos ^{-1} \sqrt{x-1}\) is
- A \([1,2]\)
- B \([0,2]\)
- C \([-1,1]\)
- D \([0,1]\)
Answer & Solution
Correct Answer
(A) \([1,2]\)
Step-by-step Solution
Detailed explanation
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 \([1,2]\).
\(\begin{array}{ll}
\therefore \quad & 0 \leq \sqrt{x-1} \leq 1 \\
& 0 \leq x-1 \leq 1 \\
& 1 \leq x \leq 2
\end{array}\)
\(\therefore\) Domain of \(f(x)\) is \([1,2]\).
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