Functions with $ f \bigg( p \Big( f \big( p ( x ) \big) \Big) \bigg) = p \bigg( f \Big( p \big( f ( x ) \big) \Big) \bigg) $ for all polynomials $ p $

score 123 · Answer 13 · 2021-04-16 06:27:25

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The functional equation $ f \left( x ^ 2 y + f ( y ) \right) = x ^ 2 f ( y ) + f \big( f ( y ) \big) $

Published on 16 Apr 2021 - 6:27

score 156 · Answer 14 · 2021-04-16 08:04:03

Solving the functional equation $ f \left( x ^ 2 + f ( y ) \right) = f \big( f ( x ) \big) + f \big( f ( y ) \big) + x ^ 2 f ( y ) + y ^ 2 f ( x ) $

score 109 · Answer 15 · 2021-04-16 08:35:41

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The functional equation $ f ^ 4 \left( x f ( x ) ^ 2 + y f ( x ) - x \right) = x ^ 3 + x f ^ 2 ( y ) - x $

Published on 16 Apr 2021 - 8:35

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Functions with $ f \bigg( p \Big( f \big( p ( x ) \big) \Big) \bigg) = p \bigg( f \Big( p \big( f ( x ) \big) \Big) \bigg) $ for all polynomials $ p $

The functional equation $ f \left( x ^ 2 y + f ( y ) \right) = x ^ 2 f ( y ) + f \big( f ( y ) \big) $

Solving the functional equation $ f \left( x ^ 2 + f ( y ) \right) = f \big( f ( x ) \big) + f \big( f ( y ) \big) + x ^ 2 f ( y ) + y ^ 2 f ( x ) $

The functional equation $ f ^ 4 \left( x f ( x ) ^ 2 + y f ( x ) - x \right) = x ^ 3 + x f ^ 2 ( y ) - x $

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