if-f-x-is-polynomial-satisfying-f-x-f-1-x-2f-x-2f-1-x-5-and-f-2-14-then-f-3-

Question Number 143427 by bramlexs22 last updated on 14/Jun/21

i f f (x) i s p o l y n o m i a l s a t i s f y i n g

f (x) f (\frac{1}{x}) - 2 f (x) + 2 f (\frac{1}{x}) = 5

a n d f (2) = 14 t h e n f (3) = ?

Answered by qaz last updated on 14/Jun/21

{\begin{cases} f (x) f (\frac{1}{x}) - 2 f (x) + 2 f (\frac{1}{x}) = 5 \dots \dots . (1) \\ f (\frac{1}{x}) f (x) - 2 f (\frac{1}{x}) + 2 f (x) = 5 \dots \dots . (2) \end{cases}

(2) - (1) ::

\Rightarrow f (x) = f (\frac{1}{x}) = \pm \sqrt{5}

how is f (2) = 14 this possible ?

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