f-1-x-2f-x-4x-3-6x-3x-2-f-x-

Question Number 91578 by jagoll last updated on 01/May/20

f (\frac{1}{x}) + 2 f (x) = \frac{4 x^{3} + 6 x}{3 x^{2}}

f (x) = ?

Commented by john santu last updated on 01/May/20

r e p l a c e x b y \frac{1}{x}

\Rightarrow f (x) + 2 f (\frac{1}{x}) = \frac{(\frac{4}{x^{3}}) + (\frac{6}{x})}{(\frac{3}{x^{2}})}

f (x) + 2 f (\frac{1}{x}) = \frac{4 + 6 x^{2}}{3 x} \dots (i i)

(i) \times 2 \Rightarrow 4 f (x) + 2 f (\frac{1}{x}) = \frac{8 x^{3} + 12 x}{3 x^{2}}

(i) - (i i)

3 f (x) = \frac{8 x^{3} + 12 x}{3 x^{2}} - \frac{6 x^{3} + 4 x}{3 x^{2}}

3 f (x) = \frac{2 x^{3} + 8 x}{3 x^{2}} = \frac{2 x^{2} + 8}{3 x}

∴ f (x) = \frac{2 x^{2} + 8}{9 x}

Commented by jagoll last updated on 01/May/20

t h a n k y o u

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