JEE Mains · Maths · STD 12 - 5. continuity and differentiation
For the differentiable function \(f: R -\{0\} \rightarrow R\), let \(3 f(x)+2 f\left(\frac{1}{x}\right)=\frac{1}{x}-10\), then \(\left|f(3)+f^{\prime}\left(\frac{1}{4}\right)\right|\) is equal to
- A \(7\)
- B \(\frac{33}{5}\)
- C \(\frac{29}{5}\)
- D \(13\)
Answer & Solution
Correct Answer
(D) \(13\)
Step-by-step Solution
Detailed explanation
\({\left[3 f(x)+2 f\left(\frac{1}{x}\right)=\frac{1}{x}-10\right] \times 3}\) \({\left[2 f(x)+3 f\left(\frac{1}{x}\right)=x-10\right] \times 2}\) \(5 f(x)=\frac{3}{x}-2 x-10\) \(f(x)=\frac{1}{5}\left(\frac{3}{x}-2 x-10\right)\)…
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