JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
If the domain of the function \( f(x)=\sin^{-1}(\frac{2}{x^{2}-2x-2}) \) is \( (-\infty,\alpha]\cup[\beta,\gamma]\cup[\delta,\infty) \), then \( \alpha+\beta+\gamma+\delta \) is equal to
- A 2
- B 4
- C 3
- D 5
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
\( -1 \le \frac{2}{x^2-2x-2} \le 1 \) \(\frac{1+x^2-2 x-2}{x^2-2 x-2} \geq 0 \Rightarrow \frac{(x-1)^2-2}{(x-1)^2-3} \geq 0\) \(\Rightarrow \frac{(x-1-\sqrt{2})(x-1+\sqrt{2})}{(x-1-\sqrt{3})(x-1+\sqrt{3})} \geq 0\)…
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