Polynomial problem

Algebra Level 4

f(x)f(x) is a polynomial satisfying the condition below.

f(x)f(1x)=f(x)+f(1x)f(x)f \left(\dfrac{1}{x}\right) = f(x) + f\left(\dfrac{1}{x}\right)

If f(10)=1001f(10) = 1001, find f(20)f(20).

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