Question

Solve the following integral equation and find closed form

score 61 · Answer 1 · 2020-04-21 22:39:09

61

Views

Solve the following integral equation and find closed form

Published on 21 Apr 2020 - 22:39

score 380 · Answer 2 · 2020-04-23 11:02:11

380

Views

What is known about the functional square root of the Riemann Zeta function?

Published on 23 Apr 2020 - 11:02

score 144 · Answer 3 · 2020-04-23 14:12:36

144

Views

How do I solve this functional equation? $ f ( m + n ) = f ( m ) + f ( n ) + 2 m n $ where $ f ( n ) $ is always a perfect square

Published on 23 Apr 2020 - 14:12

score 47 · Answer 4 · 2020-04-23 16:49:52

47

Views

$F({x+y\over 1+xy}) = F(x)\cdot F(y)$ for all real $x, y$ except $-1$

Published on 23 Apr 2020 - 16:49

score 135 · Answer 5 · 2026-03-29 04:10:54

135

Views

Which functions make it true? $(f(x)+g(x))^{-1} = f^{-1}(x) + g^{-1}(x)$

Published on 29 Mar 2026 - 4:10

score 127 · Answer 6 · 2020-04-24 11:11:43

127

Views

Determine all $f:\mathbb{R}\to\mathbb{R}$ such that $(x+y)\,\big(f(x)-f(y)\big)=f(x^2)-f(y^2)$.

Published on 24 Apr 2020 - 11:11

score 51 · Answer 7 · 2020-04-24 14:08:14

51

Views

$\frac{1}{x}f(x) = xf(\frac{1}{x})$ and $f(x+y)+1 = f(x)+f(y)$

Published on 24 Apr 2020 - 14:08

score 103 · Answer 8 · 2020-04-25 12:09:41

103

Views

find all continuous function such that $f(a)-f(b)$ is rational iff $a-b$ is rational

Published on 25 Apr 2020 - 12:09

score 1.5k · Answer 9 · 2020-04-26 06:13:15

1.5k

Views

If $f : \mathbb R \rightarrow \mathbb R $ such that $f(x^2+x)+2f(x^2-3x+2) = 9x^2-15x$. Find $f(2016)$.

Published on 26 Apr 2020 - 6:13

score 106 · Answer 10 · 2026-03-25 17:26:52

106

Views

Let $f : \mathbb R \rightarrow \mathbb R$ satisfy $f(x) \le x$ and $f(x+y) \le f(x)+f(y)$ for all $x,y \in \mathbb R$. Show that $f(x)=x$.

Published on 25 Mar 2026 - 17:26

score 40 · Answer 11 · 2020-04-26 12:59:57

40

Views

Let $f : \mathbb R \rightarrow \mathbb R$ be a continuous function such that $f(f(x)) + f(x) + x = 0$ for all $x \in \mathbb R$. Find all $f(x)$.

Published on 26 Apr 2020 - 12:59

score 142 · Answer 12 · 2020-04-27 08:51:30

142

Views

Determining ALL the functions satisfying the functional equation $f(x) + f(\frac{1}{1−x}) = \frac{2(1−2x)}{x(1−x)}$

Published on 27 Apr 2020 - 8:51

score 128 · Answer 13 · 2020-04-27 12:08:42

128

Views

Proving the uniqueness of a solution to $f(x-f(y)) = f(f(y)) + xf(y) + f(x) - 1$

Published on 27 Apr 2020 - 12:08

score 74 · Answer 14 · 2020-04-28 06:57:30

74

Views

Find the polynomial $P(x)$ s.t. for any $a,b\in\Bbb C$ s.t. $a^2+b^2=ab$, $P(a+b)=6\big(P(a)+P(b)\big)+15a^2b^2(a+b)$.

Published on 28 Apr 2020 - 6:57

score 38 · Answer 15 · 2020-04-28 15:35:04

38

Views

Checking if the solution is correct on a functional equation problem $f:\Bbb Z \rightarrow \Bbb Z$.

Published on 28 Apr 2020 - 15:35

List Question

Solve the following integral equation and find closed form

What is known about the functional square root of the Riemann Zeta function?

How do I solve this functional equation? $ f ( m + n ) = f ( m ) + f ( n ) + 2 m n $ where $ f ( n ) $ is always a perfect square

$F({x+y\over 1+xy}) = F(x)\cdot F(y)$ for all real $x, y$ except $-1$

Which functions make it true? $(f(x)+g(x))^{-1} = f^{-1}(x) + g^{-1}(x)$

Determine all $f:\mathbb{R}\to\mathbb{R}$ such that $(x+y)\,\big(f(x)-f(y)\big)=f(x^2)-f(y^2)$.

$\frac{1}{x}f(x) = xf(\frac{1}{x})$ and $f(x+y)+1 = f(x)+f(y)$

find all continuous function such that $f(a)-f(b)$ is rational iff $a-b$ is rational

If $f : \mathbb R \rightarrow \mathbb R $ such that $f(x^2+x)+2f(x^2-3x+2) = 9x^2-15x$. Find $f(2016)$.

Let $f : \mathbb R \rightarrow \mathbb R$ satisfy $f(x) \le x$ and $f(x+y) \le f(x)+f(y)$ for all $x,y \in \mathbb R$. Show that $f(x)=x$.

Let $f : \mathbb R \rightarrow \mathbb R$ be a continuous function such that $f(f(x)) + f(x) + x = 0$ for all $x \in \mathbb R$. Find all $f(x)$.

Determining ALL the functions satisfying the functional equation $f(x) + f(\frac{1}{1−x}) = \frac{2(1−2x)}{x(1−x)}$

Proving the uniqueness of a solution to $f(x-f(y)) = f(f(y)) + xf(y) + f(x) - 1$

Find the polynomial $P(x)$ s.t. for any $a,b\in\Bbb C$ s.t. $a^2+b^2=ab$, $P(a+b)=6\big(P(a)+P(b)\big)+15a^2b^2(a+b)$.

Checking if the solution is correct on a functional equation problem $f:\Bbb Z \rightarrow \Bbb Z$.

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