Question

"Compositional roots" of functions, how to define them and how many are there?

score 205 · Answer 1 · 2017-04-13 16:00:44

205

Views

"Compositional roots" of functions, how to define them and how many are there?

Published on 13 Apr 2017 - 16:00

score 49 · Answer 2 · 2026-04-03 14:08:07

49

Views

Finding the limit of a functional equation derived from $ V ( x ) = a x + b V ( c x ) $

Published on 03 Apr 2026 - 14:08

score 722 · Answer 3 · 2026-03-30 05:25:18

722

Views

Find all increasing idempotent functions on $\mathbb{R}$

Published on 30 Mar 2026 - 5:25

score 115 · Answer 4 · 2017-04-15 19:16:37

115

Views

Axiomatizing the (positive-based) exponential function

Published on 15 Apr 2017 - 19:16

score 179 · Answer 5 · 2026-02-23 15:07:43

179

Views

Is a solution of the form $f(x) = g(y)$ implicit?

Published on 23 Feb 2026 - 15:07

score 129 · Answer 6 · 2017-04-16 20:05:24

129

Views

For which continuous functions $f:\mathbb R\to\mathbb R$ does there exist a discontinuous function $g$ such that $f=g\circ g$?

Published on 16 Apr 2017 - 20:05

score 40 · Answer 7 · 2017-04-17 05:28:00

40

Views

When are there solutions to $f(x+y)-f(x-y) = axy+bx+cy+d $ and what are they?

Published on 17 Apr 2017 - 5:28

score 292 · Answer 8 · 2017-04-17 18:18:26

292

Views

A function $f:\mathbb{R^+}→\mathbb{R}$ satisfies the condition $f(ab)=f(a)+f(b)$ for $a,b>0$. prove that $f$ is continuous on $\mathbb{R^+}$.

Published on 17 Apr 2017 - 18:18

score 28 · Answer 9 · 2026-03-25 22:10:30

28

Views

Which functional equations and constraints specify f(x)=x, without directly specifying that the function is continuous or surjective

Published on 25 Mar 2026 - 22:10

score 167 · Answer 10 · 2026-03-27 01:46:40

167

Views

How does one prove, or what is required for a 'strictly monotonically increasing function'F,(1)to be continuous and (2)/or surjective

Published on 27 Mar 2026 - 1:46

score 118 · Answer 11 · 2017-04-18 12:19:56

118

Views

functional composition equations $F(F(a,b),c)=F(a,b\cdot c)$ and $F(F(a,b),c)=F(a,b^c)$

Published on 18 Apr 2017 - 12:19

score 170 · Answer 12 · 2017-04-19 06:00:49

170

Views

linearity, continuity, $F(x)=x$, and the Cauchy field automorphism equations and transcendental values

Published on 19 Apr 2017 - 6:00

score 723 · Answer 13 · 2017-04-19 16:24:36

723

Views

Functional equation with integral: $ f(x) = \int_0^x f(s) \, \mathrm ds $

Published on 19 Apr 2017 - 16:24

score 36 · Answer 14 · 2017-04-21 20:57:05

36

Views

Help with a Functional Equation / Eigenfunction Problem

Published on 21 Apr 2017 - 20:57

score 197 · Answer 15 · 2026-03-30 05:30:41

197

Views

Tricky composite function

Published on 30 Mar 2026 - 5:30

List Question

"Compositional roots" of functions, how to define them and how many are there?

Finding the limit of a functional equation derived from $ V ( x ) = a x + b V ( c x ) $

Find all increasing idempotent functions on $\mathbb{R}$

Axiomatizing the (positive-based) exponential function

Is a solution of the form $f(x) = g(y)$ implicit?

For which continuous functions $f:\mathbb R\to\mathbb R$ does there exist a discontinuous function $g$ such that $f=g\circ g$?

When are there solutions to $f(x+y)-f(x-y) = axy+bx+cy+d $ and what are they?

A function $f:\mathbb{R^+}→\mathbb{R}$ satisfies the condition $f(ab)=f(a)+f(b)$ for $a,b>0$. prove that $f$ is continuous on $\mathbb{R^+}$.

Which functional equations and constraints specify f(x)=x, without directly specifying that the function is continuous or surjective

How does one prove, or what is required for a 'strictly monotonically increasing function'F,(1)to be continuous and (2)/or surjective

functional composition equations $F(F(a,b),c)=F(a,b\cdot c)$ and $F(F(a,b),c)=F(a,b^c)$

linearity, continuity, $F(x)=x$, and the Cauchy field automorphism equations and transcendental values

Functional equation with integral: $ f(x) = \int_0^x f(s) \, \mathrm ds $

Help with a Functional Equation / Eigenfunction Problem

Tricky composite function

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