Question

Is every non-zero additive function injective/surjective?

score 48 · Answer 1 · 2023-05-17 15:26:18

48

Views

Is every non-zero additive function injective/surjective?

Published on 17 May 2023 - 15:26

score 111 · Answer 2 · 2026-03-26 07:39:04

111

Views

can anyone find me or disprove existence of an elementary function such that $f(f(x))=\sin(x)$

Published on 26 Mar 2026 - 7:39

score 55 · Answer 3 · 2023-05-18 21:00:41

55

Views

$f_n(ab) = f_n(a)f_n(b) + f_n(a-1)f_n(b-1) + f_n(a-2)f_n(b-2)+ ...+f_n(a-n)f_n(b-n)$

Published on 18 May 2023 - 21:00

score 109 · Answer 4 · 2023-05-19 11:04:30

109

Views

Find even function $f:\mathbb{R}\to\mathbb{R}$ such that $f(x)+f(x-2) = x^2-2x+1$ for all $x\in\mathbb{R}$.

Published on 19 May 2023 - 11:04

score 99 · Answer 5 · 2023-05-20 08:31:28

99

Views

Find all real functions which satisfy $xf(x+y)+f(y)=f(y)f(x+1)+f(x^2)$.

Published on 20 May 2023 - 8:31

score 67 · Answer 6 · 2023-05-21 16:36:12

67

Views

Advanced discrete functional equation

Published on 21 May 2023 - 16:36

score 61 · Answer 7 · 2023-05-22 14:24:32

61

Views

Functional equation in $R^n$

Published on 22 May 2023 - 14:24

score 129 · Answer 8 · 2023-05-22 15:28:44

129

Views

What is $f$ in $f(x)+f(1-x)=f(x^2)$?

Published on 22 May 2023 - 15:28

score 96 · Answer 9 · 2023-05-23 15:50:14

96

Views

On the system of functional equations $f(x^y)=\sqrt[y]{f(x)}$ and $ f(x^y)f(x^{-y})=1 $

Published on 23 May 2023 - 15:50

score 68 · Answer 10 · 2026-03-28 09:44:15

68

Views

Uniqueness of Binary Operations

Published on 28 Mar 2026 - 9:44

score 149 · Answer 11 · 2023-05-25 20:52:24

149

Views

Basic Functional Equation

Published on 25 May 2023 - 20:52

score 72 · Answer 12 · 2023-05-28 13:28:31

72

Views

Find $f$ such that $f(af(b))=bf(a)$

Published on 28 May 2023 - 13:28

score 120 · Answer 13 · 2023-05-29 18:16:39

120

Views

Functions that satisfy $\int_{-a}^a f(x) \ dx = a*\int_{-1}^1 f(x) \ dx$

Published on 29 May 2023 - 18:16

score 134 · Answer 14 · 2023-05-31 00:50:41

134

Views

If $f:\mathbb R\to\mathbb R$ is continuous and $f(x)f(x+2)+f(x+1)=0$ for all $x$, prove $f(x)=0$ for infinitely many $x$

Published on 31 May 2023 - 0:50

score 29 · Answer 15 · 2023-06-02 19:23:04

if we know that $y + f(y)y + 1$ goes over all real numbers once and f is bijective, can we conclude that $f(y)y$ is constant?

List Question

Is every non-zero additive function injective/surjective?

can anyone find me or disprove existence of an elementary function such that $f(f(x))=\sin(x)$

$f_n(ab) = f_n(a)f_n(b) + f_n(a-1)f_n(b-1) + f_n(a-2)f_n(b-2)+ ...+f_n(a-n)f_n(b-n)$

Find even function $f:\mathbb{R}\to\mathbb{R}$ such that $f(x)+f(x-2) = x^2-2x+1$ for all $x\in\mathbb{R}$.

Find all real functions which satisfy $xf(x+y)+f(y)=f(y)f(x+1)+f(x^2)$.

Advanced discrete functional equation

Functional equation in $R^n$

What is $f$ in $f(x)+f(1-x)=f(x^2)$?

On the system of functional equations $f(x^y)=\sqrt[y]{f(x)}$ and $ f(x^y)f(x^{-y})=1 $

Uniqueness of Binary Operations

Basic Functional Equation

Find $f$ such that $f(af(b))=bf(a)$

Functions that satisfy $\int_{-a}^a f(x) \ dx = a*\int_{-1}^1 f(x) \ dx$

If $f:\mathbb R\to\mathbb R$ is continuous and $f(x)f(x+2)+f(x+1)=0$ for all $x$, prove $f(x)=0$ for infinitely many $x$

if we know that $y + f(y)y + 1$ goes over all real numbers once and f is bijective, can we conclude that $f(y)y$ is constant?

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