Question

Find all continous functions satistying $ f(x) = f(x^{2} + \frac{x}{3} + \frac{1}{9})$ for all $x \in \mathbb{R}$

score 163 · Answer 1 · 2013-09-10 07:52:14

163

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Find all continous functions satistying $ f(x) = f(x^{2} + \frac{x}{3} + \frac{1}{9})$ for all $x \in \mathbb{R}$

Published on 10 Sep 2013 - 7:52

score 454 · Answer 2 · 2013-09-10 23:57:12

454

Views

A simple but weird functional equation

Published on 10 Sep 2013 - 23:57

score 40 · Answer 3 · 2026-04-03 16:07:56

40

Views

Assist me to obtain an equation please?

Published on 03 Apr 2026 - 16:07

score 6.4k · Answer 4 · 2013-09-12 14:34:32

6.4k

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how to solve a third degree equation of complex roots and coefficients

Published on 12 Sep 2013 - 14:34

score 1.6k · Answer 5 · 2026-04-04 12:02:02

1.6k

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Is Zorn's lemma necessary to show discontinuous $f\colon {\mathbb R} \to {\mathbb R}$ satisfying $f(x+y) = f(x) + f(y)$?

Published on 04 Apr 2026 - 12:02

score 2.6k · Answer 6 · 2013-09-16 05:21:37

2.6k

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Alternatives to percentage for measuring relative difference?

Published on 16 Sep 2013 - 5:21

score 838 · Answer 7 · 2026-03-26 02:57:40

838

Views

Functional equation for scale invariant utility functions: $f(ax)f(1/a)-f(a)f(1/a)+f(a)f(x)=0$

Published on 26 Mar 2026 - 2:57

score 2.7k · Answer 8 · 2013-09-26 12:27:55

2.7k

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Real Analysis Proofs: Additive Functions

Published on 26 Sep 2013 - 12:27

score 769 · Answer 9 · 2026-04-02 10:53:46

769

Views

Minimum period of function such that $f\left(x+\frac{13}{42}\right)+f(x)=f\left(x+\frac{1}{6}\right)+f\left(x+\frac{1}{7}\right) $

Published on 02 Apr 2026 - 10:53

score 183 · Answer 10 · 2013-09-30 03:52:05

183

Views

There is non-trivial function satisfy the given condition?

Published on 30 Sep 2013 - 3:52

score 545 · Answer 11 · 2013-09-30 06:06:26

545

Views

Solution of Equation $ 1 + x + \frac{1\cdot3}{2!}x^2 + \frac{1\cdot3\cdot5}{3!}x^3 + \ldots = \sqrt{2} $

Published on 30 Sep 2013 - 6:06

score 2.3k · Answer 12 · 2013-10-02 05:54:29

2.3k

Views

How find this function $f(1+xy)=f(x)f(y)+f(x+y)$

Published on 02 Oct 2013 - 5:54

score 72 · Answer 13 · 2013-10-02 17:15:35

72

Views

Does $f(\mathbf x _1 + \mathbf c ,...,\mathbf x _n + \mathbf c)=f(\mathbf x _1 ,...,\mathbf x _n)$ imply...

Published on 02 Oct 2013 - 17:15

score 339 · Answer 14 · 2013-10-04 07:16:09

339

Views

How to identify this power series as $k\sin(k/x)$?

Published on 04 Oct 2013 - 7:16

score 298 · Answer 15 · 2013-10-05 17:15:14

298

Views

How find all $f:\mathbb R\to\mathbb R$ such that $f\bigl(x\cdot f(y)\bigr)=y\cdot f(x)+kxy$

Published on 05 Oct 2013 - 17:15

List Question

Find all continous functions satistying $ f(x) = f(x^{2} + \frac{x}{3} + \frac{1}{9})$ for all $x \in \mathbb{R}$

A simple but weird functional equation

Assist me to obtain an equation please?

how to solve a third degree equation of complex roots and coefficients

Is Zorn's lemma necessary to show discontinuous $f\colon {\mathbb R} \to {\mathbb R}$ satisfying $f(x+y) = f(x) + f(y)$?

Alternatives to percentage for measuring relative difference?

Functional equation for scale invariant utility functions: $f(ax)f(1/a)-f(a)f(1/a)+f(a)f(x)=0$

Real Analysis Proofs: Additive Functions

Minimum period of function such that $f\left(x+\frac{13}{42}\right)+f(x)=f\left(x+\frac{1}{6}\right)+f\left(x+\frac{1}{7}\right) $

There is non-trivial function satisfy the given condition?

Solution of Equation $ 1 + x + \frac{1\cdot3}{2!}x^2 + \frac{1\cdot3\cdot5}{3!}x^3 + \ldots = \sqrt{2} $

How find this function $f(1+xy)=f(x)f(y)+f(x+y)$

Does $f(\mathbf x _1 + \mathbf c ,...,\mathbf x _n + \mathbf c)=f(\mathbf x _1 ,...,\mathbf x _n)$ imply...

How to identify this power series as $k\sin(k/x)$?

How find all $f:\mathbb R\to\mathbb R$ such that $f\bigl(x\cdot f(y)\bigr)=y\cdot f(x)+kxy$

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