List questions from functional-equations

Published on 29 Apr 2026 - 12:15

388

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Does there exist a nontrivial rational function which satisfies $f(f(f(f(x))))=x$?

Published on 10 May 2026 - 15:02

238

Views

Solving the functional equation $f(n^2+m)=f(n+m^2)$

Published on 15 Apr 2026 - 17:54

106

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Functions satisfying $f(x+y)+x= f(x)f(y)$

Published on 15 Apr 2026 - 4:44

113

Views

Property of a function with two variables: $h(x,y)=-h(y,x)$

Published on 11 Apr 2026 - 4:12

169

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Cauchy's functional equation real to real

Published on 11 Apr 2026 - 22:45

450

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Functional differential equation (FDE): $f'(x)=f(x+e)$

Published on 12 Apr 2026 - 13:37

370

Views

Do I Need To Find All Functions Satisfying A Given Equation In Such Cases?

Published on 15 Apr 2026 - 12:46

259

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Novice question: how do you approach solving an equation like this?

Published on 10 Apr 2026 - 22:22

55

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Math question related to functional equations

Published on 12 Apr 2026 - 21:46

1.2k

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Functional equation: $f(x)f(1/x) = f(x) + f(1/x)$.

Published on 14 Apr 2026 - 5:37

1.8k

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Functional equation: $ f(x^2+x+3)+2f(x^2-3x+5)= 6x^2 -10 x + 17$

Published on 16 Apr 2026 - 6:25

98

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Find all functions $ f: \mathbb{R} \to \mathbb{R} $ such that $ f(x) \geq f(y)\sin(x-y)$

Published on 17 Apr 2026 - 6:25

55

Views

Morphism, functional equations and bijection

Published on 06 May 2026 - 14:20

114

Views

Application of Cauchy Function Equation

Published on 09 Apr 2026 - 7:35

List Question

Function with Weird Property!

Does there exist a nontrivial rational function which satisfies $f(f(f(f(x))))=x$?

Solving the functional equation $f(n^2+m)=f(n+m^2)$

Functions satisfying $f(x+y)+x= f(x)f(y)$

Property of a function with two variables: $h(x,y)=-h(y,x)$

Cauchy's functional equation real to real

Functional differential equation (FDE): $f'(x)=f(x+e)$

Do I Need To Find All Functions Satisfying A Given Equation In Such Cases?

Novice question: how do you approach solving an equation like this?

Math question related to functional equations

Functional equation: $f(x)f(1/x) = f(x) + f(1/x)$.

Functional equation: $ f(x^2+x+3)+2f(x^2-3x+5)= 6x^2 -10 x + 17$

Find all functions $ f: \mathbb{R} \to \mathbb{R} $ such that $ f(x) \geq f(y)\sin(x-y)$

Morphism, functional equations and bijection

Application of Cauchy Function Equation

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