Question

Functional equation $f\big(x+f(y)\big) = f(x)-y$ where $f : \mathbb{Z} \to \mathbb{Z}$

score 362 · Answer 1 · 2016-04-29 20:30:22

362

Views

Functional equation $f\big(x+f(y)\big) = f(x)-y$ where $f : \mathbb{Z} \to \mathbb{Z}$

Published on 29 Apr 2016 - 20:30

score 101 · Answer 2 · 2016-04-30 08:29:16

101

Views

A function $f$ satisfies the condition $f[f(x) - e^x] = e + 1$ for all $x \in \Bbb R$.

Published on 30 Apr 2016 - 8:29

score 255 · Answer 3 · 2016-05-02 16:53:02

255

Views

If $g:\mathbb{N}\rightarrow \mathbb{R}$ and $g(m+n)+g(m-n)=2g(m)+2g(n)$ what is $g(x)$

Published on 02 May 2016 - 16:53

score 79 · Answer 4 · 2016-05-03 11:56:25

79

Views

How to solve this functional equation: $f(1-f(x))=1-x^{9}, f(1)=0$

Published on 03 May 2016 - 11:56

score 121 · Answer 5 · 2016-05-03 20:36:42

121

Views

continuous (on 3, 4 and 5) f is constant, if $f(x+2)+f(4x)=f(2x+1)+f(2x+2),\forall x\in\mathbb{R}$

Published on 03 May 2016 - 20:36

score 258 · Answer 6 · 2016-05-04 08:32:15

258

Views

Find all functions $f(f(f(...(f(x_1,x_2),x_3),...),x_{2016}))=x_1+x_2+...+x_{2016}$

Published on 04 May 2016 - 8:32

score 47 · Answer 7 · 2026-03-26 09:21:47

47

Views

What can be said about $f$ in $\frac{f(x,y)}{f(y,x)}=\frac{g(x,y)}{g(y,x)}$ if $g$ is known?

Published on 26 Mar 2026 - 9:21

score 437 · Answer 8 · 2026-04-02 23:40:16

437

Views

Judicious guess for the solution of differential equation $y''-6y'+9y= t^{3/2} e^{3t}$

Published on 02 Apr 2026 - 23:40

score 226 · Answer 9 · 2016-05-05 12:16:38

226

Views

Does there exist the function $f^2(x)\ge f(x+y)\left(f(x)+y \right) $

Published on 05 May 2016 - 12:16

score 2.7k · Answer 10 · 2016-05-05 16:59:04

2.7k

Views

Functional Equation: $f(x^2-y^2)=xf(x)-yf(y)$

Published on 05 May 2016 - 16:59

score 443 · Answer 11 · 2026-03-26 18:30:15

443

Views

Cauchy functional inequality

Published on 26 Mar 2026 - 18:30

score 185 · Answer 12 · 2016-05-07 11:27:49

185

Views

Number of distinct values

Published on 07 May 2016 - 11:27

score 77 · Answer 13 · 2016-05-09 06:30:29

77

Views

Functional Equations again

Published on 09 May 2016 - 6:30

score 403 · Answer 14 · 2016-05-09 08:12:56

403

Views

If $f\circ f\circ f=id$, then $f=id$

Published on 09 May 2016 - 8:12

score 63 · Answer 15 · 2016-05-10 06:23:20

63

Views

Proving a Functional Equation is Differentiable

Published on 10 May 2016 - 6:23

List Question

Functional equation $f\big(x+f(y)\big) = f(x)-y$ where $f : \mathbb{Z} \to \mathbb{Z}$

A function $f$ satisfies the condition $f[f(x) - e^x] = e + 1$ for all $x \in \Bbb R$.

If $g:\mathbb{N}\rightarrow \mathbb{R}$ and $g(m+n)+g(m-n)=2g(m)+2g(n)$ what is $g(x)$

How to solve this functional equation: $f(1-f(x))=1-x^{9}, f(1)=0$

continuous (on 3, 4 and 5) f is constant, if $f(x+2)+f(4x)=f(2x+1)+f(2x+2),\forall x\in\mathbb{R}$

Find all functions $f(f(f(...(f(x_1,x_2),x_3),...),x_{2016}))=x_1+x_2+...+x_{2016}$

What can be said about $f$ in $\frac{f(x,y)}{f(y,x)}=\frac{g(x,y)}{g(y,x)}$ if $g$ is known?

Judicious guess for the solution of differential equation $y''-6y'+9y= t^{3/2} e^{3t}$

Does there exist the function $f^2(x)\ge f(x+y)\left(f(x)+y \right) $

Functional Equation: $f(x^2-y^2)=xf(x)-yf(y)$

Cauchy functional inequality

Number of distinct values

Functional Equations again

If $f\circ f\circ f=id$, then $f=id$

Proving a Functional Equation is Differentiable

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