Question

Did I do something wrong in solving the functional equation $2f(x+y)+6y^3=f(x+2y)+x^3$ or does it have no solutions?

score 103 · Answer 1 · 2020-07-12 10:20:58

103

Views

Did I do something wrong in solving the functional equation $2f(x+y)+6y^3=f(x+2y)+x^3$ or does it have no solutions?

Published on 12 Jul 2020 - 10:20

score 133 · Answer 2 · 2020-07-12 14:18:16

133

Views

How do I finish solving $f(x)f(2y)=f(x+4y)$?

Published on 12 Jul 2020 - 14:18

score 69 · Answer 3 · 2020-07-12 18:48:27

69

Views

When the function equation $f(x)f(y)=axy+b$ is solvable

Published on 12 Jul 2020 - 18:48

score 69 · Answer 4 · 2020-07-13 07:20:41

69

Views

Does $ f(pq)\times f((1-p)(1-q))=f(p(1-q))\times f(q(1-p))$ imply $f(pq)=f(p)\times f(q)$ over $[0,1]$?

Published on 13 Jul 2020 - 7:20

score 74 · Answer 5 · 2026-02-23 12:05:46

74

Views

Finding the barrier height between two local minimums of free energy

Published on 23 Feb 2026 - 12:05

score 178 · Answer 6 · 2020-07-14 16:50:53

178

Views

Function $f$ with $f(x_1\cdot x_2)=f(x_1)+f(x_2)$ that is not $\log$?

Published on 14 Jul 2020 - 16:50

score 288 · Answer 7 · 2020-07-15 13:54:53

288

Views

find function $f$ such that $f(x)=xf(x-1)$ and $f(1) = 1$

Published on 15 Jul 2020 - 13:54

score 265 · Answer 8 · 2026-02-23 11:49:07

265

Views

Solving the functional equation $f(x)f(y)=c\,f(\sqrt{x^{2}+y^{2}})$

Published on 23 Feb 2026 - 11:49

score 1.2k · Answer 9 · 2026-03-28 22:24:19

1.2k

Views

Dirac delta solutions

Published on 28 Mar 2026 - 22:24

score 144 · Answer 10 · 2026-03-28 10:16:01

144

Views

Functional equation for $\eta(s)$ following Riemann's $2^{nd}$ method.

Published on 28 Mar 2026 - 10:16

score 319 · Answer 11 · 2020-07-17 13:29:21

319

Views

Solving functional equation $f(x)+f(1/x)=f(x)\cdot f(1/x)$

Published on 17 Jul 2020 - 13:29

score 920 · Answer 12 · 2020-07-17 19:10:13

920

Views

If $f:\mathbb{R}\setminus\{0,1\}\to\mathbb{R}$ satisfies $f(x)+2f\left(\frac 1 x\right)+3f\left(\frac x {x-1}\right)=x$, then $8f(4)=?$

Published on 17 Jul 2020 - 19:10

score 216 · Answer 13 · 2020-07-20 13:04:00

216

Views

Let $f:\mathbb{R}\to(0,\infty)$ be a differentiable function. For all $x\in\mathbb{R}$ $f'(x)=f(f(x)).$ Then show that such function does not exists

Published on 20 Jul 2020 - 13:04

score 199 · Answer 14 · 2020-07-20 14:46:04

199

Views

if $f(\frac{x+y}{2}) =\frac{f(x)+f(y)}{2}$ then find $|f(2)|$

Published on 20 Jul 2020 - 14:46

score 100 · Answer 15 · 2020-07-20 15:29:34

100

Views

Example of $f(x)-f(y)=g(x-y)$

Published on 20 Jul 2020 - 15:29

List Question

Did I do something wrong in solving the functional equation $2f(x+y)+6y^3=f(x+2y)+x^3$ or does it have no solutions?

How do I finish solving $f(x)f(2y)=f(x+4y)$?

When the function equation $f(x)f(y)=axy+b$ is solvable

Does $ f(pq)\times f((1-p)(1-q))=f(p(1-q))\times f(q(1-p))$ imply $f(pq)=f(p)\times f(q)$ over $[0,1]$?

Finding the barrier height between two local minimums of free energy

Function $f$ with $f(x_1\cdot x_2)=f(x_1)+f(x_2)$ that is not $\log$?

find function $f$ such that $f(x)=xf(x-1)$ and $f(1) = 1$

Solving the functional equation $f(x)f(y)=c\,f(\sqrt{x^{2}+y^{2}})$

Dirac delta solutions

Functional equation for $\eta(s)$ following Riemann's $2^{nd}$ method.

Solving functional equation $f(x)+f(1/x)=f(x)\cdot f(1/x)$

If $f:\mathbb{R}\setminus\{0,1\}\to\mathbb{R}$ satisfies $f(x)+2f\left(\frac 1 x\right)+3f\left(\frac x {x-1}\right)=x$, then $8f(4)=?$

Let $f:\mathbb{R}\to(0,\infty)$ be a differentiable function. For all $x\in\mathbb{R}$ $f'(x)=f(f(x)).$ Then show that such function does not exists

if $f(\frac{x+y}{2}) =\frac{f(x)+f(y)}{2}$ then find $|f(2)|$

Example of $f(x)-f(y)=g(x-y)$

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