JEE Mains · Maths · STD 12 - 1. relation and function
If the domain of the function \(f(\mathrm{x})=\frac{\cos ^{-1} \sqrt{x^{2}-x+1}}{\sqrt{\sin ^{-1}\left(\frac{2 x-1}{2}\right)}}\) is the interval \((\alpha, \beta]\), then \(\alpha+\beta\) is equal to:
- A \(2\)
- B \(\frac{3}{2}\)
- C \(\frac{1}{2}\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\(0 \leq x^{2}-x+1 \leq 1\) \(\Rightarrow x^{2}-x \leq 0\) \(\Rightarrow x \in[0,1]\) \(\text { Also, } 0\,<\,\sin ^{-1}\left(\frac{2 x-1}{2}\right) \leq \frac{\pi}{2}\) \(\Rightarrow 0\,<\,\frac{2 x-1}{2} \leq 1\) \(\Rightarrow 0\,<\,2 x-1 \leq 2\) \(1\,<\,2 x \leq 3\)…
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