MCQ
Let $3f(x) - 2f(1/x) = x,$ then $f'(2)$ is equal to
- A$2/7$
- ✓$1/2$
- C$2$
- D$7/2$
Let $1/x = y$, then $3f(1/y) - 2f(y) = 1/y$
==> $ - 2f(y) + 3f(1/y) = 1/y$
==> $ - 2f(x) + 3f(1/x) = 1/x$ .....$(ii)$
$From \,\, 3 × (i) + 2 × (ii),$
$9f(x) - 6f(1/x) - 4f(x) + 6f(1/x) = 3x + 2/x$
$5f(x) = 3x + \frac{2}{x}$
==> $f(x) = \frac{1}{5}\left[ {3x + \frac{2}{x}} \right]$
==> $f'(x) = \frac{1}{5}\left[ {3 - \frac{2}{{{x^2}}}} \right]$
==> $f'(2) = \frac{1}{5}\left[ {3 - \frac{2}{4}} \right] = \frac{1}{2}$.
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