Question

Let $3f (x) - 2 f (1/x) = x,$ then $f '(2)$ is equal to

• A. $\frac{2}{7}$
• B. $\frac{1}{2}$
• C. 2
• D. $\frac{7}{2}$

Answer 1

Answer: (B)

$3f (x) - 2 f (1/x) = x,$ .....(1)
Put $x = \frac{1}{x} , $ then $3 f\left( \frac{1}{x} \right) - 2 f(x) = \frac{1}{x}$ ....(2)
Solving (1) and (2) , we get
$5f(x) = 3x + \frac{2}{x} \Rightarrow \, f'(x) = \frac{3}{5} - \frac{2}{5x^2}$
$ \therefore \:\:\: f'(2) = \frac{3}{5} - \frac{2}{20} = \frac{1}{2}$