If f(x) be a polynomial function satisfying f(x).f (frac{1}{x}) = f(x) + f (frac{1}{x})

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1.Relation and Function

normal

If $f(x)$ be a polynomial function satisfying $f(x).f (\frac{1}{x}) = f(x) + f (\frac{1}{x})$ and $f(4) = 65$ then value of $f(6)$ is

A

$217$

B

$215$

C

$216$

D

$65$

Solution

$\because \mathrm{f}(\mathrm{x}) \cdot \mathrm{f}(1 / \mathrm{x})=\mathrm{f}(\mathrm{x})+\mathrm{f}(1 / \mathrm{x})$

$\therefore {\rm{f}}({\rm{x}}) = 1 \pm {{\rm{x}}^{\rm{n}}}\left( {{\rm{i}}{{\rm{n}}^{**}}{\rm{ star \,\,point }}} \right)$

$f(4)=65 \therefore f(x)=x^{3}+1$

$f(6)=6^{3}+1=217.$

Standard 12

Mathematics

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