A polynomial f(x0 satisfies the condition `f(x).f(1/x)=f(x)+f(1/x)` and f(10) = 1001, then the value of f(2) =?

Explanation

[9]
`f(x) = x^n + 1`
`therefore f(10) = 10^n + 1 = 1001`
`therefore 10^n = 1000 = 10^3 implies n = 3`
then `f(x) = x^2 + 1`
`therefore f(2) = (2^3 + 1) = 9`