Question

What conditions must apply for functions $f$ and $g,$ so that $f(g) = g(f)?$

score 57 · Answer 1 · 2019-09-25 17:07:43

57

Views

What conditions must apply for functions $f$ and $g,$ so that $f(g) = g(f)?$

Published on 25 Sep 2019 - 17:07

score 71 · Answer 2 · 2026-03-25 23:37:38

71

Views

When does $f(x^n) \mid (f(x))^n$? And related questions.

Published on 25 Mar 2026 - 23:37

score 57 · Answer 3 · 2019-09-26 13:37:36

57

Views

Is there a function which, composed with itself, will output $e^x$?

Published on 26 Sep 2019 - 13:37

score 160 · Answer 4 · 2026-03-25 06:11:59

160

Views

How can I find all involutions whose reciprocals are also involutions?

Published on 25 Mar 2026 - 6:11

score 236 · Answer 5 · 2019-09-28 17:29:39

236

Views

Functional equation problem: $ f \left( y ^ 2 - f ( x ) \right) = y f ( x ) ^ 2 + f \left( x ^ 2 y + y \right) $

Published on 28 Sep 2019 - 17:29

score 278 · Answer 6 · 2019-09-29 00:32:01

278

Views

Is there a continuous function such that $f(f(x)) = g(x)$?

Published on 29 Sep 2019 - 0:32

score 157 · Answer 7 · 2019-09-29 13:28:29

Solving $f(3x)=f\Big(\frac{x+y}{(x+y)^2+1}\Big)+f\Big(\frac{x-y}{(x-y)^2+1}\Big)$ and $f\big(x^2-y^2\big)=(x+y)f(x-y)+(x-y)f(x+y)$

score 189 · Answer 8 · 2019-09-29 19:50:27

189

Views

How to find all the continuous functions satisfying an equation?

Published on 29 Sep 2019 - 19:50

score 86 · Answer 9 · 2019-09-30 23:29:28

Two "incompatible" recurrence relations / functional equations: $f(y+10)=2\cdot f(y+3)-f(y)$ and $f(y+10)=\frac{10}9\cdot f(y+8)-\frac19\cdot f(y)$

score 676 · Answer 10 · 2014-03-13 01:57:53

676

Views

Multiplicative function on rationals

Published on 13 Mar 2014 - 1:57

score 72 · Answer 11 · 2014-03-14 21:33:08

72

Views

About the space $u \in C([0,T];H^{s+1}) \cap C^1([0,T];H^{s})$

Published on 14 Mar 2014 - 21:33

score 946 · Answer 12 · 2026-03-25 12:52:16

946

Views

Why computing Fatou coordinate is so hard?

Published on 25 Mar 2026 - 12:52

score 565 · Answer 13 · 2014-03-16 20:15:24

565

Views

An IMO inspired problem

Published on 16 Mar 2014 - 20:15

score 178 · Answer 14 · 2014-03-17 23:17:10

178

Views

How do you find two functions $f$ and $g$ such that $f(x) \cdot g(x)=f(x)-g(x)$?

Published on 17 Mar 2014 - 23:17

score 229 · Answer 15 · 2026-03-27 02:37:38

229

Views

Another functional equation: $f(x) + f(2x) + f(4x) = \lfloor 7x \rfloor$

Published on 27 Mar 2026 - 2:37

List Question

What conditions must apply for functions $f$ and $g,$ so that $f(g) = g(f)?$

When does $f(x^n) \mid (f(x))^n$? And related questions.

Is there a function which, composed with itself, will output $e^x$?

How can I find all involutions whose reciprocals are also involutions?

Functional equation problem: $ f \left( y ^ 2 - f ( x ) \right) = y f ( x ) ^ 2 + f \left( x ^ 2 y + y \right) $

Is there a continuous function such that $f(f(x)) = g(x)$?

Solving $f(3x)=f\Big(\frac{x+y}{(x+y)^2+1}\Big)+f\Big(\frac{x-y}{(x-y)^2+1}\Big)$ and $f\big(x^2-y^2\big)=(x+y)f(x-y)+(x-y)f(x+y)$

How to find all the continuous functions satisfying an equation?

Two "incompatible" recurrence relations / functional equations: $f(y+10)=2\cdot f(y+3)-f(y)$ and $f(y+10)=\frac{10}9\cdot f(y+8)-\frac19\cdot f(y)$

Multiplicative function on rationals

About the space $u \in C([0,T];H^{s+1}) \cap C^1([0,T];H^{s})$

Why computing Fatou coordinate is so hard?

An IMO inspired problem

How do you find two functions $f$ and $g$ such that $f(x) \cdot g(x)=f(x)-g(x)$?

Another functional equation: $f(x) + f(2x) + f(4x) = \lfloor 7x \rfloor$

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