Question

Regarding the surjectivity of a function in a functional equation

score 194 · Answer 1 · 2026-04-09 04:44:41

194

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Regarding the surjectivity of a function in a functional equation

Published on 09 Apr 2026 - 4:44

score 113 · Answer 2 · 2020-12-08 10:57:38

113

Views

Finding a function $f:(0, \infty) \to(0, \infty)$ satisfying the differential equation ${f}'\left( \frac{a}{x} \right)=\frac{x}{f\left( x \right)}$

Published on 08 Dec 2020 - 10:57

score 116 · Answer 3 · 2020-12-08 19:38:09

116

Views

A problem pertaining to functional equations with conditions $P(2020) = 2019$ and (b) $(P(x) + 1)^2 = P(x^2 + 1)$ for all $x\in\mathbb{R}$

Published on 08 Dec 2020 - 19:38

score 172 · Answer 4 · 2020-12-09 22:42:43

172

Views

Is there a non-constant function $f: \mathbb{R}_{>0} \to \mathbb{R}$ such that $f(x) = f(x + 1/x)$?

Published on 09 Dec 2020 - 22:42

score 87 · Answer 5 · 2026-04-07 23:18:52

87

Views

Interesting functional equation from a Greek math contest

Published on 07 Apr 2026 - 23:18

score 344 · Answer 6 · 2026-04-12 16:38:06

344

Views

Suppose $f(x)-f(y)=h(g(x)-g(y))$, then $h$ is linear?

Published on 12 Apr 2026 - 16:38

score 91 · Answer 7 · 2026-04-12 10:05:11

Confusing functional equation problem (application of Cauchy equation when $ f \left( \frac 1 x \right) = \frac { f ( x ) } { x ^ 2 } $)

score 100 · Answer 8 · 2020-12-12 11:19:03

100

Views

Find all functions $f(x)$ where $2f(x)+1=f(2x+1)$ for all real $x$

Published on 12 Dec 2020 - 11:19

score 46 · Answer 9 · 2020-12-15 10:12:20

46

Views

find a function that describes win percentage based on skill

Published on 15 Dec 2020 - 10:12

score 51 · Answer 10 · 2026-04-12 00:03:54

51

Views

Advection-style first order nonlinear PDE system

Published on 12 Apr 2026 - 0:03

score 153 · Answer 11 · 2020-12-16 14:41:44

153

Views

A functional equation problem: $f(xy)f\left(\frac{x+y}{xy}\right)=f(x+y)$ and $f(x+1)=f(x)+1$

Published on 16 Dec 2020 - 14:41

score 139 · Answer 12 · 2020-12-17 17:38:35

139

Views

Solutions to the functional equation $ ( x - 2 ) f ( y ) + f \big( y + 2 f ( x ) \big) = f \big( x + y f ( x ) \big) $

Published on 17 Dec 2020 - 17:38

score 949 · Answer 13 · 2020-12-18 08:40:36

949

Views

Functional equation $f(x+y)=f(x)f(y)-f(xy)+1$

Published on 18 Dec 2020 - 8:40

score 73 · Answer 14 · 2026-04-12 21:27:31

73

Views

Proving an inequality involving $L_2(\Omega)$ norms of $L_2$ and $C^{\infty}$ functions

Published on 12 Apr 2026 - 21:27

score 112 · Answer 15 · 2020-12-21 15:40:21

Find all functions $f \colon \mathbb R \to \mathbb R$ such that for $f(x)f(y) + f(\frac{1}{2} + \sqrt{xy(x + y) + \frac{1}{4}}) = f(xy) + f(x + y)$.

List Question

Regarding the surjectivity of a function in a functional equation

Finding a function $f:(0, \infty) \to(0, \infty)$ satisfying the differential equation ${f}'\left( \frac{a}{x} \right)=\frac{x}{f\left( x \right)}$

A problem pertaining to functional equations with conditions $P(2020) = 2019$ and (b) $(P(x) + 1)^2 = P(x^2 + 1)$ for all $x\in\mathbb{R}$

Is there a non-constant function $f: \mathbb{R}_{>0} \to \mathbb{R}$ such that $f(x) = f(x + 1/x)$?

Interesting functional equation from a Greek math contest

Suppose $f(x)-f(y)=h(g(x)-g(y))$, then $h$ is linear?

Confusing functional equation problem (application of Cauchy equation when $ f \left( \frac 1 x \right) = \frac { f ( x ) } { x ^ 2 } $)

Find all functions $f(x)$ where $2f(x)+1=f(2x+1)$ for all real $x$

find a function that describes win percentage based on skill

Advection-style first order nonlinear PDE system

A functional equation problem: $f(xy)f\left(\frac{x+y}{xy}\right)=f(x+y)$ and $f(x+1)=f(x)+1$

Solutions to the functional equation $ ( x - 2 ) f ( y ) + f \big( y + 2 f ( x ) \big) = f \big( x + y f ( x ) \big) $

Functional equation $f(x+y)=f(x)f(y)-f(xy)+1$

Proving an inequality involving $L_2(\Omega)$ norms of $L_2$ and $C^{\infty}$ functions

Find all functions $f \colon \mathbb R \to \mathbb R$ such that for $f(x)f(y) + f(\frac{1}{2} + \sqrt{xy(x + y) + \frac{1}{4}}) = f(xy) + f(x + y)$.

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