List questions from functional-equations

Published on 13 Apr 2026 - 1:11

64

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When can we conclude that a function is linear if a functional equation is given?

Published on 13 Apr 2026 - 0:00

289

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closed-form solution to a recursive function

Published on 10 Apr 2026 - 12:05

168

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Solving the functional equations $f(g(x)) = \sin x$ and $g(f(x)) = \cos x$

Published on 16 Apr 2026 - 10:38

116

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linear function composition

Published on 09 Apr 2026 - 16:04

156

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Find all cubic polynomials $p$ and $q$ so that $p(0)=-24,q(0)=30, p(q(x)) = q(p(x))\,\forall x\in\mathbb{R}$.

Published on 17 Apr 2026 - 9:55

108

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Functional Equation by Substitution?

Published on 09 Apr 2026 - 0:26

76

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Functional equation $f(x+y)\leq yf(x)+f(f(x)).$

Published on 13 Apr 2026 - 12:02

58

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Looking for a family of functions

Published on 12 Apr 2026 - 1:14

249

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BMO2 2019 Question 4 - Functions Problem

Published on 14 Apr 2026 - 10:51

208

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Very difficult recurrence relation for the coefficients of an ODE solution

Published on 12 Apr 2026 - 0:36

115

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How to solve this functional equation and find the integral of $f(x)$?

Published on 17 Apr 2026 - 2:15

140

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Method for solving "Iterated" functional equation

Published on 11 Apr 2026 - 8:57

128

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find the number of functions f so that $f(x+17)=f(x), f(x^2)\equiv f(x)^2+15\mod 17$ for all $x\ge 1$

Published on 17 Apr 2026 - 14:46

72

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On a functional equation that the solution is $ax^k$

Published on 09 Apr 2026 - 23:21

List Question

Involution-like functional equation $f(f(x))=ax+b$

When can we conclude that a function is linear if a functional equation is given?

closed-form solution to a recursive function

Solving the functional equations $f(g(x)) = \sin x$ and $g(f(x)) = \cos x$

linear function composition

Find all cubic polynomials $p$ and $q$ so that $p(0)=-24,q(0)=30, p(q(x)) = q(p(x))\,\forall x\in\mathbb{R}$.

Functional Equation by Substitution?

Functional equation $f(x+y)\leq yf(x)+f(f(x)).$

Looking for a family of functions

BMO2 2019 Question 4 - Functions Problem

Very difficult recurrence relation for the coefficients of an ODE solution

How to solve this functional equation and find the integral of $f(x)$?

Method for solving "Iterated" functional equation

find the number of functions f so that $f(x+17)=f(x), f(x^2)\equiv f(x)^2+15\mod 17$ for all $x\ge 1$

On a functional equation that the solution is $ax^k$

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