Question

Two-player game in the $(x,y)$ plane with points fulfulling $f(x+f(y))=y$

score 75 · Answer 1 · 2026-04-15 04:52:19

75

Views

Two-player game in the $(x,y)$ plane with points fulfulling $f(x+f(y))=y$

Published on 15 Apr 2026 - 4:52

score 111 · Answer 2 · 2026-04-17 07:52:18

111

Views

Find all $f:N_0\to N_0$ which obey the functional equation $2f(m^2+n^2)=f(m)^2+f(n)^2$ for all non-negative integers $m,n$

Published on 17 Apr 2026 - 7:52

score 137 · Answer 3 · 2026-04-17 05:34:10

137

Views

Find $f(3)$ if $f(f(x))=x^{2}+2$

Published on 17 Apr 2026 - 5:34

score 106 · Answer 4 · 2026-04-09 09:51:38

106

Views

A BDMO functional equation problem.

Published on 09 Apr 2026 - 9:51

score 328 · Answer 5 · 2026-04-17 09:21:07

328

Views

If $f(f(f(x)))+f(x)=2$ for all $0≤x≤2$ then find $\int_0^2 f(x) dx$

Published on 17 Apr 2026 - 9:21

score 91 · Answer 6 · 2026-04-16 03:20:34

91

Views

Solution of $f\bigl(x+f(y)\bigr)+f\bigl(y+f(x)\bigr)=2f\bigl(xf(y)\bigr)$

Published on 16 Apr 2026 - 3:20

score 115 · Answer 7 · 2026-04-15 20:07:04

115

Views

$f(f(n))+f(n+1)=n+2$, where $n \in \mathbb N^*_+$

Published on 15 Apr 2026 - 20:07

score 100 · Answer 8 · 2026-04-09 21:46:29

100

Views

Can we assume a function to be a polynomial in olympiads ??

Published on 09 Apr 2026 - 21:46

score 99 · Answer 9 · 2026-04-17 05:59:46

99

Views

If $f'(x)≥0$, $f''(x)≤0$ then prove that $f(x)f^{-1}(x)-x^2≤0$

Published on 17 Apr 2026 - 5:59

score 175 · Answer 10 · 2026-04-15 20:27:05

175

Views

Finding $f:\mathbb R\to\mathbb R$ which satisfies $\forall x,y\in\mathbb R,\ f(f(x+y)-f(x-y))=y^2f(x)$

Published on 15 Apr 2026 - 20:27

score 125 · Answer 11 · 2026-04-15 08:37:24

125

Views

Prove that $f(x)=x$ is the only function satisfying certain properties

Published on 15 Apr 2026 - 8:37

score 334 · Answer 12 · 2026-04-17 12:24:43

334

Views

Find all the functions $f:R\to R$ which satisfy the identity $f(x+y)+f(xy)=f(x)\cdot f(y)+1$ for all $x,y\in R$

Published on 17 Apr 2026 - 12:24

score 86 · Answer 13 · 2026-04-15 17:32:18

86

Views

Delay Functional Equation: $f(t) - f(t-\tau) = u(t)$

Published on 15 Apr 2026 - 17:32

score 187 · Answer 14 · 2026-04-16 03:51:33

functional square root problem - Solution with "Chain Solution". - 2 example problems: $f(f(x))=x^2-2$, $f(f(x))-x^2+x+3=0$ + 1 more problem

score 76 · Answer 15 · 2026-04-14 15:11:54

76

Views

If $f(x)=g(x)f(h(x))$ with $g$ and $h$ known, can I obtain $f$?

Published on 14 Apr 2026 - 15:11

List Question

Two-player game in the $(x,y)$ plane with points fulfulling $f(x+f(y))=y$

Find all $f:N_0\to N_0$ which obey the functional equation $2f(m^2+n^2)=f(m)^2+f(n)^2$ for all non-negative integers $m,n$

Find $f(3)$ if $f(f(x))=x^{2}+2$

A BDMO functional equation problem.

If $f(f(f(x)))+f(x)=2$ for all $0≤x≤2$ then find $\int_0^2 f(x) dx$

Solution of $f\bigl(x+f(y)\bigr)+f\bigl(y+f(x)\bigr)=2f\bigl(xf(y)\bigr)$

$f(f(n))+f(n+1)=n+2$, where $n \in \mathbb N^*_+$

Can we assume a function to be a polynomial in olympiads ??

If $f'(x)≥0$, $f''(x)≤0$ then prove that $f(x)f^{-1}(x)-x^2≤0$

Finding $f:\mathbb R\to\mathbb R$ which satisfies $\forall x,y\in\mathbb R,\ f(f(x+y)-f(x-y))=y^2f(x)$

Prove that $f(x)=x$ is the only function satisfying certain properties

Find all the functions $f:R\to R$ which satisfy the identity $f(x+y)+f(xy)=f(x)\cdot f(y)+1$ for all $x,y\in R$

Delay Functional Equation: $f(t) - f(t-\tau) = u(t)$

functional square root problem - Solution with "Chain Solution". - 2 example problems: $f(f(x))=x^2-2$, $f(f(x))-x^2+x+3=0$ + 1 more problem

If $f(x)=g(x)f(h(x))$ with $g$ and $h$ known, can I obtain $f$?

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