Question

The first and second variation of a given functional?

score 3.6k · Answer 1 · 2026-02-24 03:48:15

3.6k

Views

The first and second variation of a given functional?

Published on 24 Feb 2026 - 3:48

score 143 · Answer 2 · 2017-10-18 23:09:31

143

Views

Crazy Functional Equation - Possibly related to trig identities? $p(2x)=p(x)p(-x)-p(x-1)p(1-x)+4x-1$

Published on 18 Oct 2017 - 23:09

score 183 · Answer 3 · 2017-10-20 19:43:51

183

Views

Let $f:\mathbb R \to \mathbb R$ be a function, such as : $3f(x+1)-2f(2-x) = x^2 + 14x - 5$. Find $f(x)$.

Published on 20 Oct 2017 - 19:43

score 30 · Answer 4 · 2026-04-02 07:55:48

30

Views

How is $f$ restricted if we require that $f(A\cdot x)=g(A)f(x)+h(A)$?

Published on 02 Apr 2026 - 7:55

score 71 · Answer 5 · 2017-10-22 09:28:13

Find all functions $f:\Bbb R \rightarrow \Bbb R$ such that for every $x,y \in \Bbb R$: i) $f(x)\leq x$ ii) $f(x+y)\leq f(x)+f(y) $

score 59 · Answer 6 · 2017-10-24 13:19:07

59

Views

I am confused with my knowledge of polynomials?

Published on 24 Oct 2017 - 13:19

score 132 · Answer 7 · 2026-03-21 00:37:20

132

Views

If $q(x)=x^2+1$, does $q^{\circ 1/2}$ exist?

Published on 21 Mar 2026 - 0:37

score 222 · Answer 8 · 2017-10-26 07:53:46

222

Views

A suggestion on functional equations

Published on 26 Oct 2017 - 7:53

score 146 · Answer 9 · 2017-10-28 20:00:10

146

Views

Let $f: \mathbb{N} \rightarrow \mathbb{N}$ a function such that $f(mn) = f(m) + f(n)$ whenever $m$ and $n$ are relatively prime.

Published on 28 Oct 2017 - 20:00

score 268 · Answer 10 · 2017-10-30 13:11:25

268

Views

$f$ is continuous, $f(0)=1$, $f(m+n+1)=f(m)+f(n)$ for all real $m,n$. Show that $f(x)=1+x$ for all real $x$.

Published on 30 Oct 2017 - 13:11

score 691 · Answer 11 · 2017-10-30 14:50:08

691

Views

Prove there are no other solutions of functional equation $f(x+y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$

Published on 30 Oct 2017 - 14:50

score 1.9k · Answer 12 · 2017-10-31 15:40:33

1.9k

Views

Some examples of functions that are their own inverse?

Published on 31 Oct 2017 - 15:40

score 74 · Answer 13 · 2026-04-01 07:21:07

74

Views

Functional equations satisfied by the modular function $\lambda$

Published on 01 Apr 2026 - 7:21

score 99 · Answer 14 · 2026-04-06 15:42:51

99

Views

Solving recursion $f(n+1)=\frac n{n+2}f(n)$

Published on 06 Apr 2026 - 15:42

score 133 · Answer 15 · 2017-11-03 09:29:20

133

Views

let $f(\frac{x}{3})+f(\frac{2}{x})=\frac{4}{x^2}+\frac{x^2}{9}-2$ then find $f(x)$

Published on 03 Nov 2017 - 9:29

List Question

The first and second variation of a given functional?

Crazy Functional Equation - Possibly related to trig identities? $p(2x)=p(x)p(-x)-p(x-1)p(1-x)+4x-1$

Let $f:\mathbb R \to \mathbb R$ be a function, such as : $3f(x+1)-2f(2-x) = x^2 + 14x - 5$. Find $f(x)$.

How is $f$ restricted if we require that $f(A\cdot x)=g(A)f(x)+h(A)$?

Find all functions $f:\Bbb R \rightarrow \Bbb R$ such that for every $x,y \in \Bbb R$: i) $f(x)\leq x$ ii) $f(x+y)\leq f(x)+f(y) $

I am confused with my knowledge of polynomials?

If $q(x)=x^2+1$, does $q^{\circ 1/2}$ exist?

A suggestion on functional equations

Let $f: \mathbb{N} \rightarrow \mathbb{N}$ a function such that $f(mn) = f(m) + f(n)$ whenever $m$ and $n$ are relatively prime.

$f$ is continuous, $f(0)=1$, $f(m+n+1)=f(m)+f(n)$ for all real $m,n$. Show that $f(x)=1+x$ for all real $x$.

Prove there are no other solutions of functional equation $f(x+y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$

Some examples of functions that are their own inverse?

Functional equations satisfied by the modular function $\lambda$

Solving recursion $f(n+1)=\frac n{n+2}f(n)$

let $f(\frac{x}{3})+f(\frac{2}{x})=\frac{4}{x^2}+\frac{x^2}{9}-2$ then find $f(x)$

Trending Questions

Popular # Hahtags

Popular Questions