Question

Solving a functional equation arising from a probability problem: $g(kx)^2=g(x)$

score 153 · Answer 1 · 2018-12-04 01:04:59

153

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Solving a functional equation arising from a probability problem: $g(kx)^2=g(x)$

Published on 04 Dec 2018 - 1:04

score 106 · Answer 2 · 2018-12-04 01:28:58

106

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¿How to solve this functional equation: $xf(y)+yf(x)=(x+y)f(x)f(y)$? Need some help!

Published on 04 Dec 2018 - 1:28

score 42 · Answer 3 · 2018-12-05 07:21:22

42

Views

$x_i \frac{\partial f(x)}{\partial x_i} = f(x)g_i(x)$ for all $i$

Published on 05 Dec 2018 - 7:21

score 749 · Answer 4 · 2018-12-05 15:56:43

749

Views

If $f:\mathbb{R}\to\mathbb{R}$ is infinitely-differentiable, and $f(x+y)-f(y-x)=2xf^\prime(y)$, then it is a polynomial of degree less than $2$

Published on 05 Dec 2018 - 15:56

score 423 · Answer 5 · 2026-03-25 23:16:35

423

Views

$f(a)-f(b)$ is rational iff $f(a-b) $ is rational

Published on 25 Mar 2026 - 23:16

score 125 · Answer 6 · 2018-12-08 19:10:35

125

Views

Find all the bijective functions $f:[0,1]\to[0,1]$ such that $x=\frac{1}{2}\big(f(x)+f^{-1}(x)\big)$ for all $x\in[0,1]$.

Published on 08 Dec 2018 - 19:10

score 188 · Answer 7 · 2026-03-25 20:41:09

188

Views

Find function $f(x)$ that satisfying differential relation

Published on 25 Mar 2026 - 20:41

score 79 · Answer 8 · 2018-12-12 14:15:33

79

Views

Disproving a function exists

Published on 12 Dec 2018 - 14:15

score 152 · Answer 9 · 2018-12-12 16:02:22

152

Views

$f(x) * f(y) = f(x-y) + f(x+y)$

Published on 12 Dec 2018 - 16:02

score 89 · Answer 10 · 2018-12-12 16:49:14

89

Views

$f(x^2f(y)^2) = f(x^2) f(y)$

Published on 12 Dec 2018 - 16:49

score 211 · Answer 11 · 2018-12-13 06:27:41

211

Views

A doubt in the solution of IMO 1977 B3 question

Published on 13 Dec 2018 - 6:27

score 52 · Answer 12 · 2018-12-13 12:50:23

52

Views

A functional equation (another)

Published on 13 Dec 2018 - 12:50

score 121 · Answer 13 · 2018-12-13 18:02:07

121

Views

A problem with functions defined on positive integers.

Published on 13 Dec 2018 - 18:02

score 1.7k · Answer 14 · 2026-03-25 19:07:06

1.7k

Views

If $f$ be a decreasing function satisfying $f(x+y)= f(x)+ f(y)- f(x)f(y) ~\forall x, y \in \mathbb R$ and $f'(0)= -1$

Published on 25 Mar 2026 - 19:07

score 625 · Answer 15 · 2018-12-15 10:43:20

625

Views

Help in solving a simple functional equation: $3f(2x+1)=f(x) + 5x$

Published on 15 Dec 2018 - 10:43

List Question

Solving a functional equation arising from a probability problem: $g(kx)^2=g(x)$

¿How to solve this functional equation: $xf(y)+yf(x)=(x+y)f(x)f(y)$? Need some help!

$x_i \frac{\partial f(x)}{\partial x_i} = f(x)g_i(x)$ for all $i$

If $f:\mathbb{R}\to\mathbb{R}$ is infinitely-differentiable, and $f(x+y)-f(y-x)=2xf^\prime(y)$, then it is a polynomial of degree less than $2$

$f(a)-f(b)$ is rational iff $f(a-b) $ is rational

Find all the bijective functions $f:[0,1]\to[0,1]$ such that $x=\frac{1}{2}\big(f(x)+f^{-1}(x)\big)$ for all $x\in[0,1]$.

Find function $f(x)$ that satisfying differential relation

Disproving a function exists

$f(x) * f(y) = f(x-y) + f(x+y)$

$f(x^2f(y)^2) = f(x^2) f(y)$

A doubt in the solution of IMO 1977 B3 question

A functional equation (another)

A problem with functions defined on positive integers.

If $f$ be a decreasing function satisfying $f(x+y)= f(x)+ f(y)- f(x)f(y) ~\forall x, y \in \mathbb R$ and $f'(0)= -1$

Help in solving a simple functional equation: $3f(2x+1)=f(x) + 5x$

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