Question

Does a function $f$ that satisfies $f(2x+y)=f(x+1)+f(y)+4xy$ for all $x,y$ exist?

score 79 · Answer 1 · 2020-10-24 13:43:52

79

Views

Does a function $f$ that satisfies $f(2x+y)=f(x+1)+f(y)+4xy$ for all $x,y$ exist?

Published on 24 Oct 2020 - 13:43

score 86 · Answer 2 · 2020-10-24 15:29:38

86

Views

a simple functional equation $f\left(\frac{x}2\right)+f\left(\frac{x+1}2\right)=2f(x)$

Published on 24 Oct 2020 - 15:29

score 144 · Answer 3 · 2020-10-24 18:02:01

144

Views

Find all polynomial functions

Published on 24 Oct 2020 - 18:02

score 308 · Answer 4 · 2026-04-12 12:53:24

308

Views

Functional equation $f(x)f(f(x))=x^2$

Published on 12 Apr 2026 - 12:53

score 68 · Answer 5 · 2020-10-28 04:47:09

68

Views

Functional Equation (similar to Cauchy's): $ f ( x + y ) = f ( x ) f ( y ) + k x y ( x + y ) $

Published on 28 Oct 2020 - 4:47

score 135 · Answer 6 · 2026-03-26 11:01:33

135

Views

Find all functions $f$ such that $f(f(x, y), z) = f(x, yz)$

Published on 26 Mar 2026 - 11:01

score 134 · Answer 7 · 2020-10-29 16:23:07

The Functional Equation $ ( x + y ) \big( f ( x ) - f ( y ) \big) = ( x - y ) f ( x + y ) $, need solution have answer

score 47 · Answer 8 · 2026-04-11 12:56:43

47

Views

Proof of functional completeness and adequate of logical operators

Published on 11 Apr 2026 - 12:56

score 523 · Answer 9 · 2020-10-30 11:09:28

523

Views

Finding the value of $f(2001)$ given the functional equation $f\bigl(f(n)\bigr)= 3n$ and strict monotonicity of $f:\mathbb N\to\mathbb N$

Published on 30 Oct 2020 - 11:09

score 68 · Answer 10 · 2026-04-08 21:17:54

68

Views

Solving a functional equation with derivatives?

Published on 08 Apr 2026 - 21:17

score 44 · Answer 11 · 2020-10-30 21:17:09

44

Views

Another FE, reduced it to $f(x)= - f( \frac 1x)$

Published on 30 Oct 2020 - 21:17

score 85 · Answer 12 · 2020-11-01 03:08:17

85

Views

Find all $f$ such that $f(xy+f(x))=f(f(x)f(y))+x, \forall x,y\in \mathbb{R}_{>0}$

Published on 01 Nov 2020 - 3:08

score 56 · Answer 13 · 2026-04-12 03:31:58

56

Views

Can you find the other values of this function?

Published on 12 Apr 2026 - 3:31

score 815 · Answer 14 · 2026-04-09 20:32:28

815

Views

What are some real-world applications of functional equations?

Published on 09 Apr 2026 - 20:32

score 125 · Answer 15 · 2020-11-03 16:25:29

$f: \mathbb{N}\cup\{0\} \longrightarrow \mathbb{N}\cup\{0\}, \forall x\in\mathbb{N}\cup\{0\}, f(x+1)+1 = f(f(x) + 1)$

List Question

Does a function $f$ that satisfies $f(2x+y)=f(x+1)+f(y)+4xy$ for all $x,y$ exist?

a simple functional equation $f\left(\frac{x}2\right)+f\left(\frac{x+1}2\right)=2f(x)$

Find all polynomial functions

Functional equation $f(x)f(f(x))=x^2$

Functional Equation (similar to Cauchy's): $ f ( x + y ) = f ( x ) f ( y ) + k x y ( x + y ) $

Find all functions $f$ such that $f(f(x, y), z) = f(x, yz)$

The Functional Equation $ ( x + y ) \big( f ( x ) - f ( y ) \big) = ( x - y ) f ( x + y ) $, need solution have answer

Proof of functional completeness and adequate of logical operators

Finding the value of $f(2001)$ given the functional equation $f\bigl(f(n)\bigr)= 3n$ and strict monotonicity of $f:\mathbb N\to\mathbb N$

Solving a functional equation with derivatives?

Another FE, reduced it to $f(x)= - f( \frac 1x)$

Find all $f$ such that $f(xy+f(x))=f(f(x)f(y))+x, \forall x,y\in \mathbb{R}_{>0}$

Can you find the other values of this function?

What are some real-world applications of functional equations?

$f: \mathbb{N}\cup\{0\} \longrightarrow \mathbb{N}\cup\{0\}, \forall x\in\mathbb{N}\cup\{0\}, f(x+1)+1 = f(f(x) + 1)$

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