Question

Find all continuous functions $f$ : $\mathbb{R} \rightarrow \mathbb{R}$ satisfying: $f(xy)+f(x+y)=f(xy+x)+f(y)\quad\forall x,y \in \mathbb{R}$

score 1k · Answer 1 · 2013-12-14 02:40:04

Find all continuous functions $f$ : $\mathbb{R} \rightarrow \mathbb{R}$ satisfying: $f(xy)+f(x+y)=f(xy+x)+f(y)\quad\forall x,y \in \mathbb{R}$

score 635 · Answer 2 · 2013-12-16 21:29:45

635

Views

Solutions of $f(x)\cdot f(y)=f(x\cdot y)$

Published on 16 Dec 2013 - 21:29

score 144 · Answer 3 · 2013-12-17 23:57:59

144

Views

functional equations with restricted domain

Published on 17 Dec 2013 - 23:57

score 145 · Answer 4 · 2013-12-19 21:57:35

145

Views

Characterization of arithmetic mean

Published on 19 Dec 2013 - 21:57

score 2.4k · Answer 5 · 2013-12-20 06:30:16

2.4k

Views

Which $f$ satisfy the equation $\,\,f(x)\,f(y)-f(x+y)=\sin x\,\sin y\,$?

Published on 20 Dec 2013 - 6:30

score 305 · Answer 6 · 2013-12-20 17:14:07

305

Views

A functional relation which is satisfied by $\cos x$ and $\sin x$

Published on 20 Dec 2013 - 17:14

score 129 · Answer 7 · 2013-12-21 05:18:17

129

Views

How find this function $f(2^m)=?$

Published on 21 Dec 2013 - 5:18

score 272 · Answer 8 · 2013-12-21 06:20:25

272

Views

Simple functional equation: $\frac 1 2 [\alpha(x - 1) + \alpha(x + 1)]$, $\alpha(0) = 1$, $\alpha(m) = 0$

Published on 21 Dec 2013 - 6:20

score 279 · Answer 9 · 2013-12-22 02:28:18

279

Views

Galois Theory for Differential Equations?

Published on 22 Dec 2013 - 2:28

score 260 · Answer 10 · 2013-12-22 06:07:38

260

Views

show that $f(x)=c\log x $ for some $c$

Published on 22 Dec 2013 - 6:07

score 693 · Answer 11 · 2013-12-23 13:13:34

693

Views

Find $f(x)$ where $ f(x)+f\left(\frac{1-x}x\right)=x$

Published on 23 Dec 2013 - 13:13

score 216 · Answer 12 · 2013-12-24 13:35:56

216

Views

How to solve $(f'(x+1)+f'(x-1))f(x)-(f(x+1)+f(x-1))f'(x)=0$

Published on 24 Dec 2013 - 13:35

score 47 · Answer 13 · 2013-12-24 16:24:12

47

Views

Finding polynomials sattisfying $P\bigr(-c + K/(u+c)\bigl) (u+c)^2/K =P(u)$

Published on 24 Dec 2013 - 16:24

score 210 · Answer 14 · 2026-03-26 12:48:34

210

Views

Is there analytic solution to $x^y=y^x\land x\neq y$ as $y(x)$?

Published on 26 Mar 2026 - 12:48

score 138 · Answer 15 · 2013-12-25 04:39:17

138

Views

Retrieving the Taylor series for $\log$ from its functional equation

Published on 25 Dec 2013 - 4:39

List Question

Find all continuous functions $f$ : $\mathbb{R} \rightarrow \mathbb{R}$ satisfying: $f(xy)+f(x+y)=f(xy+x)+f(y)\quad\forall x,y \in \mathbb{R}$

Solutions of $f(x)\cdot f(y)=f(x\cdot y)$

functional equations with restricted domain

Characterization of arithmetic mean

Which $f$ satisfy the equation $\,\,f(x)\,f(y)-f(x+y)=\sin x\,\sin y\,$?

A functional relation which is satisfied by $\cos x$ and $\sin x$

How find this function $f(2^m)=?$

Simple functional equation: $\frac 1 2 [\alpha(x - 1) + \alpha(x + 1)]$, $\alpha(0) = 1$, $\alpha(m) = 0$

Galois Theory for Differential Equations?

show that $f(x)=c\log x $ for some $c$

Find $f(x)$ where $ f(x)+f\left(\frac{1-x}x\right)=x$

How to solve $(f'(x+1)+f'(x-1))f(x)-(f(x+1)+f(x-1))f'(x)=0$

Finding polynomials sattisfying $P\bigr(-c + K/(u+c)\bigl) (u+c)^2/K =P(u)$

Is there analytic solution to $x^y=y^x\land x\neq y$ as $y(x)$?

Retrieving the Taylor series for $\log$ from its functional equation

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