Question

Example of a non-trivial function such that $f(2x)=f(x)$

score 1.7k · Answer 1 · 2014-09-27 15:50:58

1.7k

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Example of a non-trivial function such that $f(2x)=f(x)$

Published on 27 Sep 2014 - 15:50

score 299 · Answer 2 · 2014-09-28 09:57:39

299

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Find examples of continuous functions $f:[0,1]\to[0,1]$ that satisfy $\forall x\in[0,1], f(f(x))=f(x)$ other than $f(x)=x$

Published on 28 Sep 2014 - 9:57

score 63 · Answer 3 · 2026-03-25 14:19:28

63

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How equal are two given numbers

Published on 25 Mar 2026 - 14:19

score 236 · Answer 4 · 2014-09-29 11:50:15

236

Views

Functional equation- solving techniques

Published on 29 Sep 2014 - 11:50

score 140 · Answer 5 · 2014-09-29 15:18:52

140

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Find all functions $ f:\Bbb{R}\to\Bbb{R}$ with the intermediate value property such that $\exists 1\leq n\in\Bbb{Z}, f^n(x)=-x$

Published on 29 Sep 2014 - 15:18

score 190 · Answer 6 · 2014-10-01 10:31:40

190

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The functional equation $f\bigl(m+f(n)\bigr)=f\bigl(f(m)\bigr)+f(n)$ - Understading an easy step in my solution.

Published on 01 Oct 2014 - 10:31

score 1k · Answer 7 · 2014-10-01 12:54:04

1k

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Additive involutions: $ f ( x + y ) = f ( x ) + f ( y ) $ and $ f \big( f ( x ) \big) = x $

Published on 01 Oct 2014 - 12:54

score 649 · Answer 8 · 2026-03-25 21:01:22

649

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Approximating the Digamma fucntion near 1

Published on 25 Mar 2026 - 21:01

score 11.1k · Answer 9 · 2014-10-03 20:38:54

11.1k

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$f(a+b)=f(a)+f(b)$ but $f$ is not linear

Published on 03 Oct 2014 - 20:38

score 356 · Answer 10 · 2014-10-04 08:39:31

356

Views

Solving the functional equation $f(xy)=f(f(x)+f(y))$

Published on 04 Oct 2014 - 8:39

score 64 · Answer 11 · 2026-03-28 09:53:34

64

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Proof involving the functional equation $ f ( x + n ) = f ( x ) f ( n ) $ for $ x \in \mathbb R $ and $ n \in \mathbb N $

Published on 28 Mar 2026 - 9:53

score 570 · Answer 12 · 2026-03-28 18:12:51

570

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Functional equation involving gamma function

Published on 28 Mar 2026 - 18:12

score 56 · Answer 13 · 2014-10-12 07:34:35

56

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Differentiability Problem

Published on 12 Oct 2014 - 7:34

score 5.1k · Answer 14 · 2014-10-13 06:32:40

5.1k

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Functional Equation $f(mn)=f(m)f(n)$.

Published on 13 Oct 2014 - 6:32

score 35 · Answer 15 · 2014-10-14 10:19:32

35

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Integers and functional equation

Published on 14 Oct 2014 - 10:19

List Question

Example of a non-trivial function such that $f(2x)=f(x)$

Find examples of continuous functions $f:[0,1]\to[0,1]$ that satisfy $\forall x\in[0,1], f(f(x))=f(x)$ other than $f(x)=x$

How equal are two given numbers

Functional equation- solving techniques

Find all functions $ f:\Bbb{R}\to\Bbb{R}$ with the intermediate value property such that $\exists 1\leq n\in\Bbb{Z}, f^n(x)=-x$

The functional equation $f\bigl(m+f(n)\bigr)=f\bigl(f(m)\bigr)+f(n)$ - Understading an easy step in my solution.

Additive involutions: $ f ( x + y ) = f ( x ) + f ( y ) $ and $ f \big( f ( x ) \big) = x $

Approximating the Digamma fucntion near 1

$f(a+b)=f(a)+f(b)$ but $f$ is not linear

Solving the functional equation $f(xy)=f(f(x)+f(y))$

Proof involving the functional equation $ f ( x + n ) = f ( x ) f ( n ) $ for $ x \in \mathbb R $ and $ n \in \mathbb N $

Functional equation involving gamma function

Differentiability Problem

Functional Equation $f(mn)=f(m)f(n)$.

Integers and functional equation

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