Question

Find all the $f:\mathbb{R}\rightarrow\mathbb{R}$ satisfying $f\left(f^3(x)+y^3\right)=x^2+f^3(y)$.

score 88 · Answer 1 · 2014-05-21 11:20:52

88

Views

Find all the $f:\mathbb{R}\rightarrow\mathbb{R}$ satisfying $f\left(f^3(x)+y^3\right)=x^2+f^3(y)$.

Published on 21 May 2014 - 11:20

score 3.4k · Answer 2 · 2014-05-21 14:46:23

3.4k

Views

$f,g$ such that $\int fg = \int f \int g$

Published on 21 May 2014 - 14:46

score 763 · Answer 3 · 2026-03-25 09:23:40

763

Views

A unsolved puzzle from Number Theory/ Functional inequalities

Published on 25 Mar 2026 - 9:23

score 571 · Answer 4 · 2014-05-28 23:42:21

571

Views

Are Exponential and Trigonometric Functions the Only Non-Trivial Solutions to $F'(x)=F(x+a)$?

Published on 28 May 2014 - 23:42

score 193 · Answer 5 · 2014-06-01 07:51:55

193

Views

Does the functional equation $xyF\left(xy^2,y\right)=F(x,y)$ have a unique solution?

Published on 01 Jun 2014 - 7:51

score 503 · Answer 6 · 2014-06-03 12:36:51

503

Views

All functions $g:\mathbb{N}\to\mathbb{Z}$ such that $m+n~|~g(m)+g(n)$

Published on 03 Jun 2014 - 12:36

score 1.2k · Answer 7 · 2014-06-03 18:16:48

1.2k

Views

Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.

Published on 03 Jun 2014 - 18:16

score 86 · Answer 8 · 2014-06-04 22:17:22

86

Views

Functional equations and cubes: $f\left(x^3+y^3\right)=f(x)^3+f(y)^3$

Published on 04 Jun 2014 - 22:17

score 211 · Answer 9 · 2014-06-06 15:56:40

211

Views

Find all functions $f$ such that $f\left(x^2-y^2\right)=(x-y)\big(f(x)+f(y)\big)$.

Published on 06 Jun 2014 - 15:56

score 100 · Answer 10 · 2014-06-06 19:00:32

100

Views

Functions such that $f(\frac{x+y}{2})=\frac{1}{2}f(x)+\frac{1}{2}f(y).$

Published on 06 Jun 2014 - 19:00

score 42 · Answer 11 · 2014-06-07 16:57:11

What is the function $f$ verifying $f\left(\frac{x}{2}+\frac{x}{2}\cos\left(\frac{v\pi}{x}\right)\right)=\frac{x}{2}\sin\left(\frac{v\pi}{x}\right)$?

score 105 · Answer 12 · 2026-03-25 11:12:38

105

Views

A functional equation for a Dirichlet series

Published on 25 Mar 2026 - 11:12

score 387 · Answer 13 · 2014-06-10 14:48:32

387

Views

functions satisfying $f(x)=2f(2x)$

Published on 10 Jun 2014 - 14:48

score 411 · Answer 14 · 2014-06-12 20:13:07

411

Views

Problem about functional equations: $ f \left( x ^ 2 + y \right) = f ( x ) ^ 2 + \frac { f ( x y ) } { f ( x ) } $

Published on 12 Jun 2014 - 20:13

score 567 · Answer 15 · 2014-06-13 11:48:55

567

Views

If $f$ is a strictly increasing function with $f(f(x))=x^2+2$, then $f(3)=?$

Published on 13 Jun 2014 - 11:48

List Question

Find all the $f:\mathbb{R}\rightarrow\mathbb{R}$ satisfying $f\left(f^3(x)+y^3\right)=x^2+f^3(y)$.

$f,g$ such that $\int fg = \int f \int g$

A unsolved puzzle from Number Theory/ Functional inequalities

Are Exponential and Trigonometric Functions the Only Non-Trivial Solutions to $F'(x)=F(x+a)$?

Does the functional equation $xyF\left(xy^2,y\right)=F(x,y)$ have a unique solution?

All functions $g:\mathbb{N}\to\mathbb{Z}$ such that $m+n~|~g(m)+g(n)$

Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.

Functional equations and cubes: $f\left(x^3+y^3\right)=f(x)^3+f(y)^3$

Find all functions $f$ such that $f\left(x^2-y^2\right)=(x-y)\big(f(x)+f(y)\big)$.

Functions such that $f(\frac{x+y}{2})=\frac{1}{2}f(x)+\frac{1}{2}f(y).$

What is the function $f$ verifying $f\left(\frac{x}{2}+\frac{x}{2}\cos\left(\frac{v\pi}{x}\right)\right)=\frac{x}{2}\sin\left(\frac{v\pi}{x}\right)$?

A functional equation for a Dirichlet series

functions satisfying $f(x)=2f(2x)$

Problem about functional equations: $ f \left( x ^ 2 + y \right) = f ( x ) ^ 2 + \frac { f ( x y ) } { f ( x ) } $

If $f$ is a strictly increasing function with $f(f(x))=x^2+2$, then $f(3)=?$

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