JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
The domain of the function \(f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)\) is.
- A \([1, \infty)\)
- B \((-1,2]\)
- C \([-1, \infty)\)
- D \((-\infty, 2]\)
Answer & Solution
Correct Answer
(C) \([-1, \infty)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)\) Domain \(\frac{x^{2}-3 x+2}{x^{2}+2 x+7} \geq-1\) and \(\frac{x^{2}-3 x+2}{x^{2}+2 x+7} \leq 1\) \(2 x^{2}-x+9 \geq 0\) and \(5 x \geq-5 \Rightarrow x \geq-1\) \(x \in R\) Hence Domain \(x \in[-1, \infty)\)
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