Question

Find all $f:\mathbb{R}_+\to\mathbb{R}_+$ such that $(x+y) \, f\big(f(x) \, y\big)=x^2 f\big(f(x)+f(y)\big)$ for all $x,y>0$.

score 772 · Answer 1 · 2026-04-16 21:10:07

772

Views

Find all $f:\mathbb{R}_+\to\mathbb{R}_+$ such that $(x+y) \, f\big(f(x) \, y\big)=x^2 f\big(f(x)+f(y)\big)$ for all $x,y>0$.

Published on 16 Apr 2026 - 21:10

score 50 · Answer 2 · 2026-05-10 16:57:21

50

Views

If a complicated function $F$ satisfies $F(x,y)=R(x,y)$, where $R$ is a rational function, can we safely take limits on both sides?

Published on 10 May 2026 - 16:57

score 79 · Answer 3 · 2026-04-08 18:13:23

79

Views

Functional equation $f(x)=\frac 1T \sum_{t=1}^Tf(a+tx)$

Published on 08 Apr 2026 - 18:13

score 54 · Answer 4 · 2026-04-11 16:35:50

54

Views

Solving PDE where boundary conditions explicitly expressed in equation

Published on 11 Apr 2026 - 16:35

score 826 · Answer 5 · 2026-05-10 16:12:57

826

Views

Solving the infinite radical $\sqrt{6+\sqrt{6+2\sqrt{6+3\sqrt{6+...}}}}$

Published on 10 May 2026 - 16:12

score 40 · Answer 6 · 2026-04-16 21:11:28

40

Views

Find $f,$ given that $\sum_{i=1}^n f (p_i (x_1,...,x_k))=0 $

Published on 16 Apr 2026 - 21:11

score 172 · Answer 7 · 2026-04-15 10:03:11

172

Views

$f:\mathbb Z^+\to\mathbb Z^+$ satisfying $f(n+1)\in\{4f(n)-1,f(n)-1\}$, with a unique $n\in\mathbb Z^+$ such that $f(n)=m$ for all $m\in\mathbb Z^+$

Published on 15 Apr 2026 - 10:03

score 99 · Answer 8 · 2026-04-16 15:54:58

99

Views

all functions that uphold $f'(x)=f(1/x)$

Published on 16 Apr 2026 - 15:54

score 87 · Answer 9 · 2026-04-13 20:52:37

87

Views

Summing combinations with repetition

Published on 13 Apr 2026 - 20:52

score 86 · Answer 10 · 2026-05-10 20:53:08

86

Views

About $ f(x) + c \space f(g(x)) = h(x) $

Published on 10 May 2026 - 20:53

score 139 · Answer 11 · 2026-04-17 01:55:49

139

Views

If $\int^{x}_{0}2x(f(t))^2dt = \bigg(\int^{x}_{0}2f(x-t)dt\bigg)^2$ and $f(1) = 1,$ Then $f(x)$ is

Published on 17 Apr 2026 - 1:55

score 117 · Answer 12 · 2026-04-17 07:26:25

117

Views

$0\leq f,g\in C^{1},\int_{a}^{b}\sqrt{f}\geq\int_{a}^{b}\sqrt{g}\implies\int_a^b f\geq\int_{a}^{b}g$?

Published on 17 Apr 2026 - 7:26

score 58 · Answer 13 · 2026-04-10 19:09:07

58

Views

Is it possible to solve a PDE that depends on explicit evaluations of only 1 parameter, and if so, how?

Published on 10 Apr 2026 - 19:09

score 329 · Answer 14 · 2026-04-16 23:28:18

Find all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $\varphi(f(x+y))=\varphi(f(x))+\varphi(f(y))\quad\forall x,y\in\mathbb{N}$

score 88 · Answer 15 · 2026-04-14 07:34:24

88

Views

How to solve the functional equation $f(x^n+y^n)=f(x^n)+f(y^n)$ for any positive integar $n$?

Published on 14 Apr 2026 - 7:34

List Question

Find all $f:\mathbb{R}_+\to\mathbb{R}_+$ such that $(x+y) \, f\big(f(x) \, y\big)=x^2 f\big(f(x)+f(y)\big)$ for all $x,y>0$.

If a complicated function $F$ satisfies $F(x,y)=R(x,y)$, where $R$ is a rational function, can we safely take limits on both sides?

Functional equation $f(x)=\frac 1T \sum_{t=1}^Tf(a+tx)$

Solving PDE where boundary conditions explicitly expressed in equation

Solving the infinite radical $\sqrt{6+\sqrt{6+2\sqrt{6+3\sqrt{6+...}}}}$

Find $f,$ given that $\sum_{i=1}^n f (p_i (x_1,...,x_k))=0 $

$f:\mathbb Z^+\to\mathbb Z^+$ satisfying $f(n+1)\in\{4f(n)-1,f(n)-1\}$, with a unique $n\in\mathbb Z^+$ such that $f(n)=m$ for all $m\in\mathbb Z^+$

all functions that uphold $f'(x)=f(1/x)$

Summing combinations with repetition

About $ f(x) + c \space f(g(x)) = h(x) $

If $\int^{x}_{0}2x(f(t))^2dt = \bigg(\int^{x}_{0}2f(x-t)dt\bigg)^2$ and $f(1) = 1,$ Then $f(x)$ is

$0\leq f,g\in C^{1},\int_{a}^{b}\sqrt{f}\geq\int_{a}^{b}\sqrt{g}\implies\int_a^b f\geq\int_{a}^{b}g$?

Is it possible to solve a PDE that depends on explicit evaluations of only 1 parameter, and if so, how?

Find all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $\varphi(f(x+y))=\varphi(f(x))+\varphi(f(y))\quad\forall x,y\in\mathbb{N}$

How to solve the functional equation $f(x^n+y^n)=f(x^n)+f(y^n)$ for any positive integar $n$?

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