If a function f - R -0- R is defined as 3 f x -2 f 1- x -3- x -2 x- then f -2 is equal to-1-8B- 1-4C- 1-8D- -1-4

The correct option is B 14 nbsp; nbsp;3f(x)+2f(1x)=3x+2x ⋯(1) Changing x by 1x, 3f(1x)+2f(x)=3x+2x ⋯(2) From eqn (1) and (2), f(x)=1x f'(x)= 1x^2 f”(x ...

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Standard XII

Physics

Vectors and Its Types

If a function...

Question

If a function $f : R - {0} \to R$ is defined as $3 f (x) + 2 f (\frac{1}{x}) = \frac{3}{x} + 2 x,$ then $f^{''} (2)$ is equal to

- \frac{1}{8}

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\frac{1}{4}

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\frac{1}{8}

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- \frac{1}{4}

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Solution

The correct option is B $\frac{1}{4}$
$3 f (x) + 2 f (\frac{1}{x}) = \frac{3}{x} + 2 x \dots (1)$
Changing $x$ by $\frac{1}{x}$ ,
$3 f (\frac{1}{x}) + 2 f (x) = 3 x + \frac{2}{x} \dots (2)$
From eqn $(1)$ and $(2)$ ,
$f (x) = \frac{1}{x}$
$f^{'} (x) = - \frac{1}{x^{2}}$
$f^{''} (x) = \frac{2}{x^{3}}$
$f^{''} (2) = \frac{1}{4}$

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If a function f:R−{0}→R is defined as 3f(x)+2f(1x)=3x+2x, then f′′(2) is equal to

The correct option is B 14 3f(x)+2f(1x)=3x+2x ⋯(1) Changing x by 1x, 3f(1x)+2f(x)=3x+2x ⋯(2) From eqn (1) and (2), f(x)=1x f′(x)=−1x2 f′′(x)=2x3 f′′(2)=14

If a function $f : R - {0} \to R$ is defined as $3 f (x) + 2 f (\frac{1}{x}) = \frac{3}{x} + 2 x,$ then $f^{''} (2)$ is equal to