JEE Mains · Maths · STD 12 - 6. Application of derivatives
If \(5 f(x)+4 f\left(\frac{1}{x}\right)=x^2-2, \forall x \neq 0\) and \(y=9 x^2 f(x)\), then \(y\) is strictly increasing in :
- A \(\left(0, \frac{1}{\sqrt{5}}\right) \cup\left(\frac{1}{\sqrt{5}}, \infty\right)\)
- B \(\left(-\frac{1}{\sqrt{5}}, 0\right) \cup\left(\frac{1}{\sqrt{5}}, \infty\right)\)
- C \(\left(-\frac{1}{\sqrt{5}}, 0\right) \cup\left(0, \frac{1}{\sqrt{5}}\right)\)
- D \(\left(-\infty, \frac{1}{\sqrt{5}}\right) \cup\left(0, \frac{1}{\sqrt{5}}\right)\)
Answer & Solution
Correct Answer
(B) \(\left(-\frac{1}{\sqrt{5}}, 0\right) \cup\left(\frac{1}{\sqrt{5}}, \infty\right)\)
Step-by-step Solution
Detailed explanation
\(5 \mathrm{f}(\mathrm{x})+4 \mathrm{f}\left(\frac{1}{x}\right)=\mathrm{x}^2-2, \forall x \neq 0 \)....\((1)\) Substitute \(x \rightarrow \frac{1}{x}\) \(5 f\left(\frac{1}{x}\right)+4 f(x)=\frac{1}{x^2}-2\) \(....(2)\) On solving \((1)\) and \((2)\)…
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