List questions from functional-equations

Published on 01 Apr 2026 - 22:24

75

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Determine function such that $f\left(\sqrt{x_1^2+(f(x_1))^2}\right) = f\left(\sqrt{x_2^2+(f(x_2))^2}\right)$ for every $x_1,x_2$.

Published on 03 Jun 2015 - 17:31

136

Views

Solve the system of functional equations.

Published on 03 Jun 2015 - 18:59

132

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Solving an equation for a function: $1-\frac{f(x)}{f(ax)} = (1-a)^2x^2$

Published on 04 Jun 2015 - 1:32

4.1k

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Is $f(x) = Cx\log x$ the only solution to $f(xy) = xf(y) + yf(x)$?

Published on 05 Jun 2015 - 8:19

202

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Functions proof.

Published on 05 Jun 2015 - 16:04

342

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Solve the functional equation $\frac{f(x)}{f(y)}=f\left( \frac{x-y}{f(y)} \right)$

Published on 06 Jun 2015 - 11:15

126

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Easily computable function that is one-to-one and onto with 2 or more inputs

Published on 11 Jun 2015 - 5:38

155

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If $f(f(x)) = x $ has at most 1 solution, then so does $f(x) = x$.

Published on 25 Mar 2026 - 16:13

112

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Polynomials $f(x)$ such that $f(x)f(x-1)+f(x^2)=0$

Published on 12 Jun 2015 - 7:25

445

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Way to solve basic functional equations

Published on 12 Jun 2015 - 8:01

52

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Generalized Functional Equation

Published on 15 Jun 2015 - 8:53

96

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Find all $f:\mathbb{R}\rightarrow\mathbb{R}$ for which $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$

Published on 21 Jun 2015 - 22:41

39

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Representation of a Functional Equation.

Published on 22 Jun 2015 - 12:13

22

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Find a derivative of equation that contains Fourier series

Published on 22 Jun 2015 - 18:54

List Question

How to solve non-linear differential equation

Determine function such that $f\left(\sqrt{x_1^2+(f(x_1))^2}\right) = f\left(\sqrt{x_2^2+(f(x_2))^2}\right)$ for every $x_1,x_2$.

Solve the system of functional equations.

Solving an equation for a function: $1-\frac{f(x)}{f(ax)} = (1-a)^2x^2$

Is $f(x) = Cx\log x$ the only solution to $f(xy) = xf(y) + yf(x)$?

Functions proof.

Solve the functional equation $\frac{f(x)}{f(y)}=f\left( \frac{x-y}{f(y)} \right)$

Easily computable function that is one-to-one and onto with 2 or more inputs

If $f(f(x)) = x $ has at most 1 solution, then so does $f(x) = x$.

Polynomials $f(x)$ such that $f(x)f(x-1)+f(x^2)=0$

Way to solve basic functional equations

Generalized Functional Equation

Find all $f:\mathbb{R}\rightarrow\mathbb{R}$ for which $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$

Representation of a Functional Equation.

Find a derivative of equation that contains Fourier series

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