JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
The domain of the function \(f(x)=\sin ^{-1}\left[2 x^{2}-3\right]+\log _{2}\left(\log _{\frac{1}{2}}\left(x^{2}-5 x+5\right)\right)\) where \([ t ]\) is the greatest integer function, is.
- A \(\left(-\sqrt{\frac{5}{2}}, \frac{5-\sqrt{5}}{2}\right)\)
- B \(\left(\frac{5-\sqrt{5}}{2}, \frac{5+\sqrt{5}}{2}\right)\)
- C \(\left(1, \frac{5-\sqrt{5}}{2}\right)\)
- D \(\left[1, \frac{5+\sqrt{5}}{2}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(1, \frac{5-\sqrt{5}}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\sin ^{-1}\left[2 x^{2}-3\right]+\log _{2}\left(\log _{\frac{1}{2}}\left(x^{2}-5 x+5\right)\right)\) \(P_{1}:-1 \leq\left[2 x^{2}-3\right]<1\) \(\Rightarrow-1 \leq 2 x ^{2}-3<2\) \(\Rightarrow 2<2 x ^{2}<5\) \(\Rightarrow 1< x ^{2}<\frac{5}{2}\)…
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