JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Considering only the principal values of the inverse trigonometric functions, the domain of the function \(f(x)=\cos ^{-1}\left(\frac{x^{2}-4 x+2}{x^{2}+3}\right)\) is.
- A \(\left(-\infty, \frac{1}{4}\right]\)
- B \(\left[-\frac{1}{4}, \infty\right)\)
- C \(\left(-\frac{1}{3}, \infty\right)\)
- D \(\left(-\infty, \frac{1}{3}\right]\)
Answer & Solution
Correct Answer
(B) \(\left[-\frac{1}{4}, \infty\right)\)
Step-by-step Solution
Detailed explanation
\(\left|\frac{x^{2}+4 x+2}{x^{2}+3}\right| \leq 1\) \(\left(x^{2}-4 x+2\right)^{2} \leq\left(x^{2}+3\right)^{2}\) \(\left(x^{2}-4 x+2\right)^{2}-\left(x^{2}+3\right)^{2} \leq 0\) \(\left(2 x^{2}-4 x+5\right)(-4 x-1) \leq 0\) \(-4 x-1 \leq 0 \rightarrow x \geq-\frac{1}{4}\)
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