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# If 2f (X) − 3 F ( 1 X ) = X 2 (X ≠ 0), Then F(2) is Equal to (A) − 7 4 (B) 5 2(C) −1 (D) None of These - CBSE (Science) Class 11 - Mathematics

#### Question

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

• (a)  $- \frac{7}{4}$

• (b)  $\frac{5}{2}$

• (c) −1

• (d) None of these

#### Solution

(a)  $- \frac{7}{4}$

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

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

Is there an error in this question or solution?

#### APPEARS IN

Solution If 2f (X) − 3 F ( 1 X ) = X 2 (X ≠ 0), Then F(2) is Equal to (A) − 7 4 (B) 5 2(C) −1 (D) None of These Concept: Functions.
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