Question

Functional equation high school problem $f(x) = f(-x) - 2x $

score 72 · Answer 1 · 2016-09-20 16:19:03

72

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Functional equation high school problem $f(x) = f(-x) - 2x $

Published on 20 Sep 2016 - 16:19

score 84 · Answer 2 · 2016-09-21 13:15:59

84

Views

Find a derivable function $f$ for which $f(x) - f(x-1) =\alpha ( f(x-1) - f(x-2) )$

Published on 21 Sep 2016 - 13:15

score 5.2k · Answer 3 · 2016-09-22 12:56:56

5.2k

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How to solve $f(f(x)) = x$?

Published on 22 Sep 2016 - 12:56

score 33 · Answer 4 · 2016-09-22 22:48:01

33

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Am I allowed to make these kinds of substitutions?

Published on 22 Sep 2016 - 22:48

score 908 · Answer 5 · 2026-03-27 00:56:16

908

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Extremising a functional with boundary conditions (Euler-Lagrange)

Published on 27 Mar 2026 - 0:56

score 219 · Answer 6 · 2016-09-22 23:18:26

219

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Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that $5f(x+y)+y^5=f(x)+(x+y)^5$?

Published on 22 Sep 2016 - 23:18

score 164 · Answer 7 · 2016-09-23 05:16:50

164

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Find the function $f(x)$ if $f(x+2f(y))=f(x)+y+f(y)$

Published on 23 Sep 2016 - 5:16

score 827 · Answer 8 · 2016-09-23 12:25:38

827

Views

Determine all functions $f$ satisfying the functional relation $f(x)+f\left(\frac{1}{1-x}\right)=\frac{2(1-2x)}{x(1-x)}$

Published on 23 Sep 2016 - 12:25

score 242 · Answer 9 · 2016-09-25 08:15:29

242

Views

How find the function if such $f(P(x)+Q(f(y))+Q(y)P(f(x)))=Q(y)+P(f(x))+P(x)Q(f(y))$

Published on 25 Sep 2016 - 8:15

score 126 · Answer 10 · 2016-09-25 14:53:09

126

Views

In search of nontrivial solutions to $f'(t)=f(t/2)$

Published on 25 Sep 2016 - 14:53

score 2k · Answer 11 · 2016-09-25 16:04:09

2k

Views

Function with derivative-like property: $f(ab) = af(b) + bf(a)$

Published on 25 Sep 2016 - 16:04

score 2.3k · Answer 12 · 2016-09-27 05:54:32

2.3k

Views

How would I prove that this function is affine if $f(x+h)-f(x)=hf'(x)$?

Published on 27 Sep 2016 - 5:54

score 545 · Answer 13 · 2016-09-27 12:56:00

545

Views

The functional equation $f(x+x) = f(x)f(x)$

Published on 27 Sep 2016 - 12:56

score 488 · Answer 14 · 2016-09-27 22:43:05

488

Views

Does a function that satisfies the equality $f(a+b) = f(a)f(b)$ have to be exponential?

Published on 27 Sep 2016 - 22:43

score 124 · Answer 15 · 2016-09-28 22:33:27

124

Views

Solving the multiplicative functional equation $f(x)\cdot f\left(\frac{1}{1-x}\right)=x, \; \forall x \neq 0,1.$

Published on 28 Sep 2016 - 22:33

List Question

Functional equation high school problem $f(x) = f(-x) - 2x $

Find a derivable function $f$ for which $f(x) - f(x-1) =\alpha ( f(x-1) - f(x-2) )$

How to solve $f(f(x)) = x$?

Am I allowed to make these kinds of substitutions?

Extremising a functional with boundary conditions (Euler-Lagrange)

Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that $5f(x+y)+y^5=f(x)+(x+y)^5$?

Find the function $f(x)$ if $f(x+2f(y))=f(x)+y+f(y)$

Determine all functions $f$ satisfying the functional relation $f(x)+f\left(\frac{1}{1-x}\right)=\frac{2(1-2x)}{x(1-x)}$

How find the function if such $f(P(x)+Q(f(y))+Q(y)P(f(x)))=Q(y)+P(f(x))+P(x)Q(f(y))$

In search of nontrivial solutions to $f'(t)=f(t/2)$

Function with derivative-like property: $f(ab) = af(b) + bf(a)$

How would I prove that this function is affine if $f(x+h)-f(x)=hf'(x)$?

The functional equation $f(x+x) = f(x)f(x)$

Does a function that satisfies the equality $f(a+b) = f(a)f(b)$ have to be exponential?

Solving the multiplicative functional equation $f(x)\cdot f\left(\frac{1}{1-x}\right)=x, \; \forall x \neq 0,1.$

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