Question

Find all real functions $f:\mathbf{R} \to \mathbf{R}$ satisfying the relation $f(x^2+y(f(x)))=x(f(x+y))$.

score 145 · Answer 1 · 2016-11-28 17:38:42

145

Views

Find all real functions $f:\mathbf{R} \to \mathbf{R}$ satisfying the relation $f(x^2+y(f(x)))=x(f(x+y))$.

Published on 28 Nov 2016 - 17:38

score 449 · Answer 2 · 2026-03-29 21:36:35

449

Views

How To Determine the Constants Based on Characteristics of the Graph

Published on 29 Mar 2026 - 21:36

score 113 · Answer 3 · 2026-02-23 13:47:30

113

Views

Functional Derivative in Concordance function (copula theory)

Published on 23 Feb 2026 - 13:47

score 148 · Answer 4 · 2016-12-02 11:48:58

148

Views

Find all function $ f:\Bbb R\to\Bbb R$ such that $ f(x+y)f(x-y)=(f(x)+f(y))^2-4x^2f(y)$.

Published on 02 Dec 2016 - 11:48

score 102 · Answer 5 · 2016-12-02 20:26:58

102

Views

Finding $f$ such that $f(x)+f(y)=f\left(\frac{x+y}{1-xy}\right)$

Published on 02 Dec 2016 - 20:26

score 1.1k · Answer 6 · 2026-03-27 00:37:45

1.1k

Views

Uniqueness of the solution of Fredholm's integral equation

Published on 27 Mar 2026 - 0:37

score 35 · Answer 7 · 2016-12-06 18:45:31

35

Views

Find function $f(ax+b)+c \le x \le f(x+c)+b$

Published on 06 Dec 2016 - 18:45

score 83 · Answer 8 · 2016-12-07 15:26:17

83

Views

If $f$ continuous and $[f(x_1)+...+f(x_n)]/n=f([x_1+...+x_n]/n)$ then $f$ linear

Published on 07 Dec 2016 - 15:26

score 226 · Answer 9 · 2016-12-07 19:22:22

226

Views

continuous function in a triangle

Published on 07 Dec 2016 - 19:22

score 82 · Answer 10 · 2016-12-08 03:56:02

82

Views

$f(x+y)f(x-y)=[f(x)f(y)]^2$ implies $f(x)=g\left(x^2\right)$ for some $g$

Published on 08 Dec 2016 - 3:56

score 244 · Answer 11 · 2016-12-08 13:38:55

244

Views

Find all the functions $f:\mathbb R\rightarrow \mathbb R$, such that $f\left(x+2^y\right)=f(x)+2^{f(y)}$

Published on 08 Dec 2016 - 13:38

score 129 · Answer 12 · 2016-12-08 16:03:54

129

Views

Evaluate $\int_{0}^{x} f(t)dt$

Published on 08 Dec 2016 - 16:03

score 153 · Answer 13 · 2016-12-09 12:36:33

153

Views

Finding existence of $ f : N → N $ with the following properties: $f(1) = 2$ and $f(f(n)) = f(n)+n (n ∈ N).$

Published on 09 Dec 2016 - 12:36

score 188 · Answer 14 · 2016-12-10 00:42:46

188

Views

No function $f:\mathbb{Z}\rightarrow \{1, 2, 3\}$ satisfying $f(x)\ne f(y)$ for all integers $x,y$ and $|x-y|\in\{2, 3, 5\}$

Published on 10 Dec 2016 - 0:42

score 109 · Answer 15 · 2016-12-10 01:44:46

109

Views

Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$

Published on 10 Dec 2016 - 1:44

List Question

Find all real functions $f:\mathbf{R} \to \mathbf{R}$ satisfying the relation $f(x^2+y(f(x)))=x(f(x+y))$.

How To Determine the Constants Based on Characteristics of the Graph

Functional Derivative in Concordance function (copula theory)

Find all function $ f:\Bbb R\to\Bbb R$ such that $ f(x+y)f(x-y)=(f(x)+f(y))^2-4x^2f(y)$.

Finding $f$ such that $f(x)+f(y)=f\left(\frac{x+y}{1-xy}\right)$

Uniqueness of the solution of Fredholm's integral equation

Find function $f(ax+b)+c \le x \le f(x+c)+b$

If $f$ continuous and $[f(x_1)+...+f(x_n)]/n=f([x_1+...+x_n]/n)$ then $f$ linear

continuous function in a triangle

$f(x+y)f(x-y)=[f(x)f(y)]^2$ implies $f(x)=g\left(x^2\right)$ for some $g$

Find all the functions $f:\mathbb R\rightarrow \mathbb R$, such that $f\left(x+2^y\right)=f(x)+2^{f(y)}$

Evaluate $\int_{0}^{x} f(t)dt$

Finding existence of $ f : N → N $ with the following properties: $f(1) = 2$ and $f(f(n)) = f(n)+n (n ∈ N).$

No function $f:\mathbb{Z}\rightarrow \{1, 2, 3\}$ satisfying $f(x)\ne f(y)$ for all integers $x,y$ and $|x-y|\in\{2, 3, 5\}$

Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$

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