List questions from functional-equations

Published on 06 Dec 2017 - 19:03

132

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Given $g(x)$, is there a function $f(x)$ so that $f(x) - f(x-1) = g(x)$?

Published on 06 Dec 2017 - 20:16

59

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Existence of a Functional Equation

Published on 07 Dec 2017 - 14:39

485

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Challenging problem about $f : \mathbb{R}^2 \rightarrow \mathbb{R}$ such that $f(x,y)+f(y,z)+f(z,x) = 0$ for all real $x, y, z$

Published on 08 Dec 2017 - 5:48

102

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How to prove $f(x)$ is continuous is on $\Bbb R$?

Published on 08 Dec 2017 - 12:09

103

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Proof showing if $f(\frac{3x-2}{2})=x^2-x-1,$ find $f(0)=?$

Published on 08 Dec 2017 - 18:25

569

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Entire functions such that $\frac{f(z+1)-f(z-1)}{2}=f'(z)$

Published on 10 Dec 2017 - 18:58

296

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Making a rigorous argument on the series of mobius function?

Published on 27 Mar 2026 - 14:10

239

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Prove that $f$ is constant if $f(x)=f(x^2-x+1)$

Published on 11 Dec 2017 - 20:50

434

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Solve $f(x+f(2y))=f(x)+f(y)+y$

Published on 14 Dec 2017 - 13:12

80

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Functional equation analysis of a continuous function

Published on 07 Apr 2026 - 17:14

503

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Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(xy - 1) + f(x)f(y) = 2xy - 1$

Published on 22 Dec 2017 - 13:58

120

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Functional puzzle: find $f(2)$

Published on 22 Dec 2017 - 17:35

215

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Tripling an involution (Functional equation)

Published on 08 Apr 2026 - 11:43

304

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Find all "tame" solutions of $f(x+y)+f(x-y)=2(f(x)+f(y))$

Published on 24 Dec 2017 - 18:46

List Question

Differentiable functions $f'(x)=f(-x)^4f(x)$

Given $g(x)$, is there a function $f(x)$ so that $f(x) - f(x-1) = g(x)$?

Existence of a Functional Equation

Challenging problem about $f : \mathbb{R}^2 \rightarrow \mathbb{R}$ such that $f(x,y)+f(y,z)+f(z,x) = 0$ for all real $x, y, z$

How to prove $f(x)$ is continuous is on $\Bbb R$?

Proof showing if $f(\frac{3x-2}{2})=x^2-x-1,$ find $f(0)=?$

Entire functions such that $\frac{f(z+1)-f(z-1)}{2}=f'(z)$

Making a rigorous argument on the series of mobius function?

Prove that $f$ is constant if $f(x)=f(x^2-x+1)$

Solve $f(x+f(2y))=f(x)+f(y)+y$

Functional equation analysis of a continuous function

Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(xy - 1) + f(x)f(y) = 2xy - 1$

Functional puzzle: find $f(2)$

Tripling an involution (Functional equation)

Find all "tame" solutions of $f(x+y)+f(x-y)=2(f(x)+f(y))$

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