JEE Mains · Maths · STD 12 - 1. relation and function
The domain of the function \(f(x)=\frac{\cos ^{-1}\left(\frac{x^{2}-5 x+6}{x^{2}-9}\right)}{\log _{e}\left(x^{2}-3 x+2\right)} \text { is }\)
- A \((-\infty, 1) \cup(2, \infty)\)
- B \((2, \infty)\)
- C \(\left[-\frac{1}{2}, 1\right) \cup(2, \infty)\)
- D \(\left[-\frac{1}{2}, 1\right) \cup(2, \infty)-\left\{\frac{3+\sqrt{5}}{2}, \frac{3-\sqrt{5}}{2}\right\}\)
Answer & Solution
Correct Answer
(D) \(\left[-\frac{1}{2}, 1\right) \cup(2, \infty)-\left\{\frac{3+\sqrt{5}}{2}, \frac{3-\sqrt{5}}{2}\right\}\)
Step-by-step Solution
Detailed explanation
\(-1 \leq \frac{x^{2}-5 x+6}{x^{2}-9} \leq 1\) \(\frac{x^{2}-5 x+6}{x^{2}-9}-1 \leq 0\) \(\frac{1}{x+3} \geq 0\) \(x \in(-3, \infty) \ldots \ldots(1)\) \(\frac{x^{2}-5 x+6}{x^{2}-9}+1 \geq 0\) \(\frac{2 x+1}{x+3} \geq 0\)…
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