Question

If 2f (x) − \[3f\left( \frac{1}{x} \right) = x^2\] (x ≠ 0), then f(2) is equal to

 

विकल्प

• (a)  \[- \frac{7}{4}\]

   

• (b)  \[\frac{5}{2}\]

   

• (c) −1

• (d) None of these

   

Answer 1

(a)  \[- \frac{7}{4}\]

2f (x) − \[3f\left( \frac{1}{x} \right) = x^2\]  (x ≠ 0)                  ....(1)

\[\text{ Replacing x by } \frac{1}{x}: \]
\[2f\left( \frac{1}{x} \right) - 3f(x) = \frac{1}{x^2} . . . (2) \]
\[\text{ Solving equations (1) & (2) } \]
\[ - 5f (x) = \frac{3} {x^2} + 2 x^2 \]
\[ \Rightarrow f(x) = \frac{- 1}{5} \left( \frac{3}{x^2} + 2 x^2 \right)\]
\[\text{ Thus } , f(2) = \frac{- 1}{5} \left( \frac{3}{4} + 2 \times 4 \right)\]
\[ = \frac{- 1}{5} \left( \frac{3 + 32}{4} \right) \]
\[ = \frac{- 7}{4}\]