List questions from functional-equations

Published on 23 Jun 2019 - 5:22

74

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Functions $f$ that $f(f(x))=x$, but $f:S^1\to S^1$

Published on 25 Mar 2026 - 2:28

201

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$f:\mathbb{R_{\geq 0}} \to \mathbb{R_{\geq 0}}$ such that for all $x$ we have $xf(1+xf(y))=f(f(x)+f(y))$

Published on 23 Jun 2019 - 10:39

162

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Find all functions for $f:\Bbb{N}\to\Bbb{N}$ such that $f\left(m^2+f(n)\right)=f\left(m^2\right) +n$

Published on 23 Jun 2019 - 11:13

1.2k

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Injectivity and surjectivity of a recursive function

Published on 24 Jun 2019 - 23:35

55

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Prove that there exists a continuous function $f(\!x\!):\mathbb{R}\rightarrow\mathbb{R}$ so that the following functional equation holds.

Published on 27 Jun 2019 - 3:54

58

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Two variable function equations

Published on 27 Jun 2019 - 6:38

167

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Analytical method to solve the given equations

Published on 27 Jun 2019 - 15:03

78

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A Computational Functional Equation Problem: $ f ( x ) f \big( f ( x ) \big) = 1 $

Published on 29 Jun 2019 - 21:00

183

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What are the continuous solutions to the functional equation $f(x) = \tfrac{1}{2}f(x^2)+\tfrac{1}{2}f(2x-x^2)$?

Published on 01 Jul 2019 - 18:10

193

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Prove that $f(x)=x$.

Published on 27 Mar 2026 - 1:44

672

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Minimum possible value of $f(2007)$ where $f(m f(n)) = n f(m)$, $m,n\in \Bbb N$

Published on 25 Mar 2026 - 7:45

53

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Functional equation with two inputs: $f(x,y)f(y,x)=1$

Published on 05 Jul 2019 - 23:19

172

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A functional-differential equation

Published on 25 Mar 2026 - 15:45

70

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Differential Equations Question involving $f(x+y)$

Published on 11 Jul 2019 - 12:49

List Question

Functional equation for tan

Functions $f$ that $f(f(x))=x$, but $f:S^1\to S^1$

$f:\mathbb{R_{\geq 0}} \to \mathbb{R_{\geq 0}}$ such that for all $x$ we have $xf(1+xf(y))=f(f(x)+f(y))$

Find all functions for $f:\Bbb{N}\to\Bbb{N}$ such that $f\left(m^2+f(n)\right)=f\left(m^2\right) +n$

Injectivity and surjectivity of a recursive function

Prove that there exists a continuous function $f(\!x\!):\mathbb{R}\rightarrow\mathbb{R}$ so that the following functional equation holds.

Two variable function equations

Analytical method to solve the given equations

A Computational Functional Equation Problem: $ f ( x ) f \big( f ( x ) \big) = 1 $

What are the continuous solutions to the functional equation $f(x) = \tfrac{1}{2}f(x^2)+\tfrac{1}{2}f(2x-x^2)$?

Prove that $f(x)=x$.

Minimum possible value of $f(2007)$ where $f(m f(n)) = n f(m)$, $m,n\in \Bbb N$

Functional equation with two inputs: $f(x,y)f(y,x)=1$

A functional-differential equation

Differential Equations Question involving $f(x+y)$

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