Question

A functional equation: $4f(x)^3 +f(3x)=3f(x)$

score 777 · Answer 1 · 2015-03-14 19:52:04

777

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A functional equation: $4f(x)^3 +f(3x)=3f(x)$

Published on 14 Mar 2015 - 19:52

score 432 · Answer 2 · 2026-03-29 15:21:33

432

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What special role plays the function $\pi^{\frac x\pi}$ in analysis?

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score 269 · Answer 3 · 2015-03-15 12:08:30

269

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Defining a rectangular prism using a formula and complex numbers.

Published on 15 Mar 2015 - 12:08

score 573 · Answer 4 · 2026-04-02 21:00:37

573

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Calculus of Variations for discrete functionals

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score 1.1k · Answer 5 · 2015-03-20 12:07:11

1.1k

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Prove that function is continuous without knowing the function explicitly

Published on 20 Mar 2015 - 12:07

score 197 · Answer 6 · 2015-03-21 17:48:53

197

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How to solve the delay algebraic equation $xf(x) + \alpha f(x - {x_0}) - \alpha f(x + {x_0}) = 0$?

Published on 21 Mar 2015 - 17:48

score 114 · Answer 7 · 2015-03-22 18:12:06

114

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Find all continuous functions $f:\mathbb{R}\to\mathbb{R}$ satisfying $\frac{f(x+3)}{3+f(x)}=\frac{4+x^2}{x^2}$

Published on 22 Mar 2015 - 18:12

score 65 · Answer 8 · 2015-03-22 19:06:52

65

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Is there a function $f:\mathbb{R}\to\mathbb{R}$ such that $f\circ f\circ f=Id.$, but $f\neq Id.$?

Published on 22 Mar 2015 - 19:06

score 3k · Answer 9 · 2015-03-23 19:01:03

3k

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Solving $(f(x))^2 = f(\sqrt{2}x)$

Published on 23 Mar 2015 - 19:01

score 114 · Answer 10 · 2015-03-24 08:42:21

114

Views

Follow-up to $f(x)^2 = f(\sqrt2 x)$

Published on 24 Mar 2015 - 8:42

score 615 · Answer 11 · 2015-03-25 10:29:00

615

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BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$

Published on 25 Mar 2015 - 10:29

score 386 · Answer 12 · 2015-03-25 12:48:49

386

Views

$f(\alpha x) = f(x)^{\beta}$ under different constraints

Published on 25 Mar 2015 - 12:48

score 55 · Answer 13 · 2026-03-27 15:16:28

55

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score 493 · Answer 14 · 2015-03-27 03:36:24

493

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Proving existence and uniqueness of solutions to the functional equation $f(n) = r \cdot f(n-1)$

Published on 27 Mar 2015 - 3:36

score 73 · Answer 15 · 2015-03-27 07:18:10

73

Views

A problem on solving functional equations

Published on 27 Mar 2015 - 7:18

List Question

A functional equation: $4f(x)^3 +f(3x)=3f(x)$

What special role plays the function $\pi^{\frac x\pi}$ in analysis?

Defining a rectangular prism using a formula and complex numbers.

Calculus of Variations for discrete functionals

Prove that function is continuous without knowing the function explicitly

How to solve the delay algebraic equation $xf(x) + \alpha f(x - {x_0}) - \alpha f(x + {x_0}) = 0$?

Find all continuous functions $f:\mathbb{R}\to\mathbb{R}$ satisfying $\frac{f(x+3)}{3+f(x)}=\frac{4+x^2}{x^2}$

Is there a function $f:\mathbb{R}\to\mathbb{R}$ such that $f\circ f\circ f=Id.$, but $f\neq Id.$?

Solving $(f(x))^2 = f(\sqrt{2}x)$

Follow-up to $f(x)^2 = f(\sqrt2 x)$

BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$

$f(\alpha x) = f(x)^{\beta}$ under different constraints

Solving a linear functional equation

Proving existence and uniqueness of solutions to the functional equation $f(n) = r \cdot f(n-1)$

A problem on solving functional equations

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