Given a polynomial f(x) of n degree such that f(x)+f(1x)=f(x)⋅f(1/x) Find the polynomial

Deborah Proctor 2022-10-14 Answered
Given a polynomial f ( x ) of n degree such that
f ( x ) + f ( 1 x ) = f ( x ) f ( 1 x )
Find the polynomial
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Answers (1)

driogairea1
Answered 2022-10-15 Author has 16 answers
f ( y ) = 1 + y
f ( x ) + f ( 1 x ) = 1 + x + 1 + 1 x = 2 + x + 1 x
f ( x ) f ( 1 x ) = ( 1 + x ) ( 1 + 1 x ) = 1 + x + 1 x + x 1 x = 2 + x + 1 x
In fact, f ( y ) = 1 + y k for k N seems to work for the same reason.
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