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If f(x) is a polynomial function satisfy...

If `f(x)` is a polynomial function satisfying `f(x)dotf(1/x)=f(x)+f(1/x)` and `f(4)=65 ,t h e nfin df(6)dot`

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Polynomial function satisfying
`f(x)*f((1)/(x))=f(x) +f((1)/(x))`
is `f(x)= +-x^(n)+1`
` :. f(4)= +-4^(n)+1=65`
or `4^(n)+1=65`
or `4^(n)=64`
or `n=3`
So, `f(x)=x^(3)=1.`
Hence, `f(6)=6^(3)+1=217`
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