Question

Rigorously prove that $f(x) = x^k$ is the only rational function that satisfies a given equation.

score 102 · Answer 1 · 2026-03-29 06:30:23

102

Views

Rigorously prove that $f(x) = x^k$ is the only rational function that satisfies a given equation.

Published on 29 Mar 2026 - 6:30

score 277 · Answer 2 · 2019-10-05 09:13:12

277

Views

Function such that $f(f(f(x))) = f(f(x)) \neq f(x)$

Published on 05 Oct 2019 - 9:13

score 61 · Answer 3 · 2019-10-07 02:10:31

61

Views

Procedure of solving a two variables polynomial?

Published on 07 Oct 2019 - 2:10

score 116 · Answer 4 · 2026-03-25 17:19:18

116

Views

Can someone provide an example of a shift operator solving a delay differential equation?

Published on 25 Mar 2026 - 17:19

score 103 · Answer 5 · 2019-10-07 18:30:03

103

Views

Cauchy equation $ f ( x + y ) = f ( x ) + f ( y ) $ with an additional condition $ f \left( \frac 1 x \right) = \frac 1 { x ^ 2 } f ( x ) $

Published on 07 Oct 2019 - 18:30

score 111 · Answer 6 · 2019-10-08 16:14:37

111

Views

How to solve this functional equation

Published on 08 Oct 2019 - 16:14

score 443 · Answer 7 · 2019-10-08 21:54:11

443

Views

Defining sine and cosine from functional equations $(S(x))^2+(C(x))^2=1$, $C(x+y)=C(x)C(y)-S(x)S(y)$, etc

Published on 08 Oct 2019 - 21:54

score 55 · Answer 8 · 2019-10-09 20:06:26

55

Views

Curious equation I came up with

Published on 09 Oct 2019 - 20:06

score 359 · Answer 9 · 2019-10-12 21:48:17

359

Views

Find all $f:\mathbb{N} \to \mathbb{N}$ such that $f(n) + f\big(f(n)\big) = 6n$ for every $n\in\mathbb{N}$.

Published on 12 Oct 2019 - 21:48

score 28 · Answer 10 · 2026-02-23 06:36:26

28

Views

Differentiable probability distribution on $\mathbb{R}$ with the minimim variance

Published on 23 Feb 2026 - 6:36

score 141 · Answer 11 · 2019-10-13 12:54:03

141

Views

Find polynomials in real $x$

Published on 13 Oct 2019 - 12:54

score 750 · Answer 12 · 2026-03-28 16:14:12

750

Views

Determine all functions $f:\mathbb{Z}\to\mathbb{Z}$ such that $f\big(f(n)\big)=-(q-p)\,f(n)+pq\,n$ for all $n\in\mathbb{Z}$.

Published on 28 Mar 2026 - 16:14

score 164 · Answer 13 · 2026-03-26 11:01:35

164

Views

How to find $f(x)$ in weird integral equation $ \int _ 0 ^ 1 f ( x ) c ^ x \ \mathrm d x = c $

Published on 26 Mar 2026 - 11:01

score 31 · Answer 14 · 2019-10-18 16:41:31

31

Views

Prove that $f$ belongs to $B(X,\mathbb C)$ and evaluate $\Vert f \Vert$.

Published on 18 Oct 2019 - 16:41

score 599 · Answer 15 · 2019-10-18 18:03:46

599

Views

Find all functions $ f: \mathbb{R} \to \mathbb{R}$ satisfying $f(x + y) = x + f(y)$

Published on 18 Oct 2019 - 18:03

List Question

Rigorously prove that $f(x) = x^k$ is the only rational function that satisfies a given equation.

Function such that $f(f(f(x))) = f(f(x)) \neq f(x)$

Procedure of solving a two variables polynomial?

Can someone provide an example of a shift operator solving a delay differential equation?

Cauchy equation $ f ( x + y ) = f ( x ) + f ( y ) $ with an additional condition $ f \left( \frac 1 x \right) = \frac 1 { x ^ 2 } f ( x ) $

How to solve this functional equation

Defining sine and cosine from functional equations $(S(x))^2+(C(x))^2=1$, $C(x+y)=C(x)C(y)-S(x)S(y)$, etc

Curious equation I came up with

Find all $f:\mathbb{N} \to \mathbb{N}$ such that $f(n) + f\big(f(n)\big) = 6n$ for every $n\in\mathbb{N}$.

Differentiable probability distribution on $\mathbb{R}$ with the minimim variance

Find polynomials in real $x$

Determine all functions $f:\mathbb{Z}\to\mathbb{Z}$ such that $f\big(f(n)\big)=-(q-p)\,f(n)+pq\,n$ for all $n\in\mathbb{Z}$.

How to find $f(x)$ in weird integral equation $ \int _ 0 ^ 1 f ( x ) c ^ x \ \mathrm d x = c $

Prove that $f$ belongs to $B(X,\mathbb C)$ and evaluate $\Vert f \Vert$.

Find all functions $ f: \mathbb{R} \to \mathbb{R}$ satisfying $f(x + y) = x + f(y)$

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