Question

Series expansion for function satisfying a functional equation

score 84 · Answer 1 · 2026-04-08 17:36:43

84

Views

Series expansion for function satisfying a functional equation

Published on 08 Apr 2026 - 17:36

score 114 · Answer 2 · 2026-04-13 18:18:27

114

Views

Is it feasible to use Operator Calculus to solve for $f(t)=\underbrace{\exp(\exp(\dots\exp}_{t}(0)\dots))$ over $\mathbb{R}$

Published on 13 Apr 2026 - 18:18

score 40 · Answer 3 · 2026-04-16 01:15:08

40

Views

Analytical solution to $e^{f(x^{\alpha+1})}=e^{f(x)}e^{f(x^\alpha)}$ other than $f(x)=\log{x^\lambda}$

Published on 16 Apr 2026 - 1:15

score 205 · Answer 4 · 2026-04-16 00:29:06

205

Views

Find $f(7)$ given $f(x)f(y)=f(x+y)+f(x-y)$ and $f(1)=3$

Published on 16 Apr 2026 - 0:29

score 66 · Answer 5 · 2026-04-14 02:27:30

66

Views

Prove that $f$ equals the constant function $1$.

Published on 14 Apr 2026 - 2:27

score 182 · Answer 6 · 2026-04-16 08:37:37

182

Views

Find the number of functions $f(x)$ with $f(f(n)) = n+2022$ for every nonnegative integer n.

Published on 16 Apr 2026 - 8:37

score 371 · Answer 7 · 2026-04-10 03:09:25

371

Views

Is it possible to deduce the derivatives of sine and cosine without geometry and "cheating?"

Published on 10 Apr 2026 - 3:09

score 76 · Answer 8 · 2026-04-15 19:49:04

76

Views

Find all valid functions $f:\mathcal{T}\to\mathcal{S}$

Published on 15 Apr 2026 - 19:49

score 81 · Answer 9 · 2026-04-15 07:18:55

81

Views

Examples of functions with linearity that are not polynomials or derivatives?

Published on 15 Apr 2026 - 7:18

score 34 · Answer 10 · 2026-04-14 22:54:20

34

Views

is there a nonpolynomial function $g$ so that $g(p,y)\in \mathbb{Q}[y], g(x,q) \in \mathbb{Q}[x]\forall p,q\in \mathbb{Q}$

Published on 14 Apr 2026 - 22:54

score 134 · Answer 11 · 2026-04-16 03:08:54

134

Views

show that $f(x)=x$ where $\,\forall x,y\in\mathbb{R}^+, f(x+f(y+xy)) = (y+1)f(x+1)-1$

Published on 16 Apr 2026 - 3:08

score 139 · Answer 12 · 2026-04-16 06:46:36

139

Views

show there is no function $f:\mathbb{R}\to\mathbb{R}$ so that $f(0) > 0$ and $f(x+y)\ge f(x)+yf(f(x))\,\forall x,y\in\mathbb{R}$

Published on 16 Apr 2026 - 6:46

score 54 · Answer 13 · 2026-04-11 21:59:26

54

Views

Find coefficient in series expansion of $x^2C^3(x)$

Published on 11 Apr 2026 - 21:59

score 535 · Answer 14 · 2026-04-16 19:06:33

535

Views

Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ where $f(xf(y)+f(x)+y)=xy+f(x)+f(y)$

Published on 16 Apr 2026 - 19:06

score 109 · Answer 15 · 2026-04-17 02:53:13

109

Views

find all $f:\mathbb{R}\to\mathbb{R}$ so that $|f(x+y)-f(x-y) - y|\leq y^2$ for all $x,y\in\mathbb{R}$

Published on 17 Apr 2026 - 2:53

List Question

Series expansion for function satisfying a functional equation

Is it feasible to use Operator Calculus to solve for $f(t)=\underbrace{\exp(\exp(\dots\exp}_{t}(0)\dots))$ over $\mathbb{R}$

Analytical solution to $e^{f(x^{\alpha+1})}=e^{f(x)}e^{f(x^\alpha)}$ other than $f(x)=\log{x^\lambda}$

Find $f(7)$ given $f(x)f(y)=f(x+y)+f(x-y)$ and $f(1)=3$

Prove that $f$ equals the constant function $1$.

Find the number of functions $f(x)$ with $f(f(n)) = n+2022$ for every nonnegative integer n.

Is it possible to deduce the derivatives of sine and cosine without geometry and "cheating?"

Find all valid functions $f:\mathcal{T}\to\mathcal{S}$

Examples of functions with linearity that are not polynomials or derivatives?

is there a nonpolynomial function $g$ so that $g(p,y)\in \mathbb{Q}[y], g(x,q) \in \mathbb{Q}[x]\forall p,q\in \mathbb{Q}$

show that $f(x)=x$ where $\,\forall x,y\in\mathbb{R}^+, f(x+f(y+xy)) = (y+1)f(x+1)-1$

show there is no function $f:\mathbb{R}\to\mathbb{R}$ so that $f(0) > 0$ and $f(x+y)\ge f(x)+yf(f(x))\,\forall x,y\in\mathbb{R}$

Find coefficient in series expansion of $x^2C^3(x)$

Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ where $f(xf(y)+f(x)+y)=xy+f(x)+f(y)$

find all $f:\mathbb{R}\to\mathbb{R}$ so that $|f(x+y)-f(x-y) - y|\leq y^2$ for all $x,y\in\mathbb{R}$

Trending Questions

Popular # Hahtags

Popular Questions