Question

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

score 68 · Answer 1 · 2026-04-14 14:51:11

68

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

Published on 14 Apr 2026 - 14:51

score 72 · Answer 2 · 2026-04-09 18:56:02

72

Views

An equation involving first order derivate

Published on 09 Apr 2026 - 18:56

score 121 · Answer 3 · 2026-04-13 07:37:49

121

Views

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

Published on 13 Apr 2026 - 7:37

score 116 · Answer 4 · 2026-04-29 12:24:29

116

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 29 Apr 2026 - 12:24

score 141 · Answer 5 · 2026-04-28 17:07:07

141

Views

Proof of asymptotics of a recursion or functional equation

Published on 28 Apr 2026 - 17:07

score 82 · Answer 6 · 2026-04-08 23:38:29

82

Views

Manipulating a functional equation

Published on 08 Apr 2026 - 23:38

score 69 · Answer 7 · 2026-04-17 08:55:44

69

Views

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

Published on 17 Apr 2026 - 8:55

score 445 · Answer 8 · 2026-04-29 12:28:43

445

Views

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

Published on 29 Apr 2026 - 12:28

score 724 · Answer 9 · 2026-04-17 12:24:00

724

Views

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

Published on 17 Apr 2026 - 12:24

score 169 · Answer 10 · 2026-04-15 07:28:43

169

Views

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

Published on 15 Apr 2026 - 7:28

score 115 · Answer 11 · 2026-04-11 17:50:58

115

Views

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

Published on 11 Apr 2026 - 17:50

score 43 · Answer 12 · 2026-04-13 22:30:11

43

Views

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

Published on 13 Apr 2026 - 22:30

score 414 · Answer 13 · 2026-04-13 19:28:02

414

Views

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

Published on 13 Apr 2026 - 19:28

score 78 · Answer 14 · 2026-04-12 12:26:11

78

Views

Verifying the given answer does not work

Published on 12 Apr 2026 - 12:26

score 53 · Answer 15 · 2026-04-14 01:12:33

53

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 14 Apr 2026 - 1:12

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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