Question

Find the number of functions $f:\mathbb Q \rightarrow\mathbb Q$ satisfying the following conditions:

score 69 · Answer 1 · 2023-10-23 13:59:34

69

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Find the number of functions $f:\mathbb Q \rightarrow\mathbb Q$ satisfying the following conditions:

Published on 23 Oct 2023 - 13:59

score 111 · Answer 2 · 2026-04-02 04:25:50

111

Views

Solving an "almost differential" equation

Published on 02 Apr 2026 - 4:25

score 52 · Answer 3 · 2023-10-24 08:32:57

52

Views

Coupled functions $f,g$ satisfy $Lf(\lambda) = \frac{\beta}{\beta + \lambda} Lg(\lambda)$, solve for $f$

Published on 24 Oct 2023 - 8:32

score 175 · Answer 4 · 2023-10-25 16:02:04

175

Views

Do linearity & Leibniz imply differentiation?

Published on 25 Oct 2023 - 16:02

score 31 · Answer 5 · 2023-10-25 16:42:51

31

Views

Examples of functional equations where the sought solution is bijective

Published on 25 Oct 2023 - 16:42

score 75 · Answer 6 · 2023-10-26 14:20:19

75

Views

How to solve the functional equation $f(x + y) = f(x) + g(y)$ for all $x, y \in \mathbf{R}$?

Published on 26 Oct 2023 - 14:20

score 103 · Answer 7 · 2026-03-25 21:45:03

103

Views

A characterization of the floor function

Published on 25 Mar 2026 - 21:45

score 144 · Answer 8 · 2023-10-28 20:41:32

144

Views

How to solve the functional equation $3f(-x)+f(x)+f(\frac{1}{x})=x$

Published on 28 Oct 2023 - 20:41

score 633 · Answer 9 · 2023-10-28 22:23:40

633

Views

Solving functional equation using inverses

Published on 28 Oct 2023 - 22:23

score 137 · Answer 10 · 2026-02-23 13:37:48

137

Views

Integer series related to the functional differential equation $f'(x) = f(f(x))$

Published on 23 Feb 2026 - 13:37

score 115 · Answer 11 · 2023-10-30 21:05:39

115

Views

How to solve functional equation $f(x^{2}) = \frac{f(x)}{1 + x}$?

Published on 30 Oct 2023 - 21:05

score 82 · Answer 12 · 2023-10-31 20:24:18

82

Views

Show that there is $c \in (-1,2)$ such that $f'(c)=0$.

Published on 31 Oct 2023 - 20:24

score 95 · Answer 13 · 2023-11-01 05:16:38

95

Views

Solving the functional equation $f\left(x\right)+f\left(\frac{x-1}{x}\right)=1+x$

Published on 01 Nov 2023 - 5:16

score 115 · Answer 14 · 2023-11-01 14:49:57

115

Views

Solving functional equations $2f(x) g(y) \pm f(x)^2 \pm g(y)^2 = 2 \sqrt{a} h(x \pm y) \pm (a+b)$

Published on 01 Nov 2023 - 14:49

score 170 · Answer 15 · 2023-11-05 04:21:37

170

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To find all functions which satisfy$f(x^3)+f^3(y)+f^3(z)=3xyz \\ \forall x+y+z=0$ and $x,y,z\in\mathbb R$

Published on 05 Nov 2023 - 4:21

List Question

Find the number of functions $f:\mathbb Q \rightarrow\mathbb Q$ satisfying the following conditions:

Solving an "almost differential" equation

Coupled functions $f,g$ satisfy $Lf(\lambda) = \frac{\beta}{\beta + \lambda} Lg(\lambda)$, solve for $f$

Do linearity & Leibniz imply differentiation?

Examples of functional equations where the sought solution is bijective

How to solve the functional equation $f(x + y) = f(x) + g(y)$ for all $x, y \in \mathbf{R}$?

A characterization of the floor function

How to solve the functional equation $3f(-x)+f(x)+f(\frac{1}{x})=x$

Solving functional equation using inverses

Integer series related to the functional differential equation $f'(x) = f(f(x))$

How to solve functional equation $f(x^{2}) = \frac{f(x)}{1 + x}$?

Show that there is $c \in (-1,2)$ such that $f'(c)=0$.

Solving the functional equation $f\left(x\right)+f\left(\frac{x-1}{x}\right)=1+x$

Solving functional equations $2f(x) g(y) \pm f(x)^2 \pm g(y)^2 = 2 \sqrt{a} h(x \pm y) \pm (a+b)$

To find all functions which satisfy$f(x^3)+f^3(y)+f^3(z)=3xyz \\ \forall x+y+z=0$ and $x,y,z\in\mathbb R$

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