Question

Functional Equations and information theory: $f(xy)=f(x)f(y)$ for all $x,y\in[0,1]$

score 65 · Answer 1 · 2018-01-25 12:24:08

65

Views

Functional Equations and information theory: $f(xy)=f(x)f(y)$ for all $x,y\in[0,1]$

Published on 25 Jan 2018 - 12:24

score 69 · Answer 2 · 2026-03-17 10:38:24

69

Views

An equation involving first order derivate

Published on 17 Mar 2026 - 10:38

score 118 · Answer 3 · 2026-03-17 13:14:58

118

Views

How Do I solve $f(x)^2=f(2x)$ analytically?

Published on 17 Mar 2026 - 13:14

score 108 · Answer 4 · 2026-03-22 09:10:24

108

Views

Let $f: \mathbb{R} \to \mathbb{R}$ and $\exists \ \ b \in \mathbb{R} : f(x+b)=\sqrt{f(x)-f^2(x)}+\frac{1}{2}$

Published on 22 Mar 2026 - 9:10

score 136 · Answer 5 · 2026-03-17 20:09:56

136

Views

Proof of asymptotics of a recursion or functional equation

Published on 17 Mar 2026 - 20:09

score 78 · Answer 6 · 2026-03-17 00:44:12

78

Views

Manipulating a functional equation

Published on 17 Mar 2026 - 0:44

score 66 · Answer 7 · 2026-03-17 09:02:17

66

Views

Number of functions in $g(g(x))=g(x)$

Published on 17 Mar 2026 - 9:02

score 439 · Answer 8 · 2026-03-23 03:26:18

439

Views

Is there a less-trivial integer function with described properties?

Published on 23 Mar 2026 - 3:26

score 721 · Answer 9 · 2018-01-31 12:11:35

721

Views

Find all functions $ f:\mathbb{R} \mapsto \mathbb{R} $ such that $f[x^2+f(y)] = y +[f(x)]^2$

Published on 31 Jan 2018 - 12:11

score 167 · Answer 10 · 2018-02-02 10:01:54

167

Views

Find all possible values for $f(2018)$ if $f(x)\cdot f(y)=f(x-y)$

Published on 02 Feb 2018 - 10:01

score 112 · Answer 11 · 2026-03-17 20:56:13

112

Views

Is there a not increasing function such that $f(f(n))=n+2$?

Published on 17 Mar 2026 - 20:56

score 40 · Answer 12 · 2026-03-17 11:01:03

40

Views

Proving $p^2=q$ given a functional equation

Published on 17 Mar 2026 - 11:01

score 410 · Answer 13 · 2026-03-16 21:02:41

410

Views

What is the value of $f(100)$?

Published on 16 Mar 2026 - 21:02

score 75 · Answer 14 · 2026-03-17 04:56:30

75

Views

Verifying the given answer does not work

Published on 17 Mar 2026 - 4:56

score 50 · Answer 15 · 2018-02-07 13:22:27

50

Views

$T$ is an integrate operator on $C[0,1]$,$ Tx=y$,$Ty=x$, here $x$,$y$ are positive on $[0,1]$, show $x=y$

Published on 07 Feb 2018 - 13:22

List Question

Functional Equations and information theory: $f(xy)=f(x)f(y)$ for all $x,y\in[0,1]$

An equation involving first order derivate

How Do I solve $f(x)^2=f(2x)$ analytically?

Let $f: \mathbb{R} \to \mathbb{R}$ and $\exists \ \ b \in \mathbb{R} : f(x+b)=\sqrt{f(x)-f^2(x)}+\frac{1}{2}$

Proof of asymptotics of a recursion or functional equation

Manipulating a functional equation

Number of functions in $g(g(x))=g(x)$

Is there a less-trivial integer function with described properties?

Find all functions $ f:\mathbb{R} \mapsto \mathbb{R} $ such that $f[x^2+f(y)] = y +[f(x)]^2$

Find all possible values for $f(2018)$ if $f(x)\cdot f(y)=f(x-y)$

Is there a not increasing function such that $f(f(n))=n+2$?

Proving $p^2=q$ given a functional equation

What is the value of $f(100)$?

Verifying the given answer does not work

$T$ is an integrate operator on $C[0,1]$,$ Tx=y$,$Ty=x$, here $x$,$y$ are positive on $[0,1]$, show $x=y$

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