Question

A question on functional equation

score 66 · Answer 1 · 2017-12-25 02:46:49

66

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A question on functional equation

Published on 25 Dec 2017 - 2:46

score 106 · Answer 2 · 2017-12-25 11:49:15

106

Views

$ f \left( f ( x ) ^ 2 + y \right) = x ^2 + f ( y ) $ converts into Cauchy.

Published on 25 Dec 2017 - 11:49

score 272 · Answer 3 · 2026-04-03 03:37:57

272

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Finding period of $f$ using the functional equation $f(x) + f(x+a+b) = f(x+a) + f(x+b)$

Published on 03 Apr 2026 - 3:37

score 57 · Answer 4 · 2017-12-27 12:08:38

57

Views

$f(x-y) = f(x)f(y)$ defined from $\mathbb{R}\to\mathbb{R}$ and $f(x)\ge 0$ for all $x$. find $f(3)$

Published on 27 Dec 2017 - 12:08

score 625 · Answer 5 · 2017-12-28 04:00:02

625

Views

Find all functions $f:\mathbb{R} \mapsto \mathbb{R}$ which satisfy $f(x^2+y f(z)) =x f(x) + z f(y)$

Published on 28 Dec 2017 - 4:00

score 75 · Answer 6 · 2017-12-28 07:04:20

75

Views

How many functions satisfy $f_7(x)=x$?

Published on 28 Dec 2017 - 7:04

score 433 · Answer 7 · 2017-12-28 18:26:32

433

Views

Function taking on all values thrice

Published on 28 Dec 2017 - 18:26

score 83 · Answer 8 · 2017-12-28 19:38:12

Check to see if the function $f$ which satisfies the following relation is one-to-one or not: $\forall x,y\in \Bbb R: f(x+f(y))=f(x)+y$

score 192 · Answer 9 · 2017-12-29 08:03:17

Can we assume $ f ( y ) = 0 $ in solving the functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $?

score 131 · Answer 10 · 2017-12-29 13:30:54

131

Views

If $f(x) $ is a continuous function with a given identity, how do I find $f(\sqrt{3})$?

Published on 29 Dec 2017 - 13:30

score 58 · Answer 11 · 2017-12-30 20:36:56

58

Views

Verify injectiveness of the function $f:\Bbb R\rightarrow \Bbb R$ satisfying the following: $f(x)=2x-(f(x))^2$

Published on 30 Dec 2017 - 20:36

score 59 · Answer 12 · 2017-12-31 11:37:33

59

Views

Given that $f(x)+f(y) = f[x \times \sqrt{1-y^2}+ y\times \sqrt{1-x^2}]$ To prove $f(4x^3-3x) + 3f(x) = 0$

Published on 31 Dec 2017 - 11:37

score 87 · Answer 13 · 2017-12-31 12:54:55

87

Views

$ |f(x) - f(y)| \le 7| x-y |^{201} $ I need to find a linear relation between $f(101)$ and $f(200)$

Published on 31 Dec 2017 - 12:54

score 198 · Answer 14 · 2018-01-01 05:14:08

198

Views

Verify surjectivity of the function $f$ satisfying: $f(x)+f(x^2)=x$

Published on 01 Jan 2018 - 5:14

score 108 · Answer 15 · 2018-01-01 15:02:56

108

Views

How to interpret the functional identity $f(a+b)=f(a)+f(b)$?

Published on 01 Jan 2018 - 15:02

List Question

A question on functional equation

$ f \left( f ( x ) ^ 2 + y \right) = x ^2 + f ( y ) $ converts into Cauchy.

Finding period of $f$ using the functional equation $f(x) + f(x+a+b) = f(x+a) + f(x+b)$

$f(x-y) = f(x)f(y)$ defined from $\mathbb{R}\to\mathbb{R}$ and $f(x)\ge 0$ for all $x$. find $f(3)$

Find all functions $f:\mathbb{R} \mapsto \mathbb{R}$ which satisfy $f(x^2+y f(z)) =x f(x) + z f(y)$

How many functions satisfy $f_7(x)=x$?

Function taking on all values thrice

Check to see if the function $f$ which satisfies the following relation is one-to-one or not: $\forall x,y\in \Bbb R: f(x+f(y))=f(x)+y$

Can we assume $ f ( y ) = 0 $ in solving the functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $?

If $f(x) $ is a continuous function with a given identity, how do I find $f(\sqrt{3})$?

Verify injectiveness of the function $f:\Bbb R\rightarrow \Bbb R$ satisfying the following: $f(x)=2x-(f(x))^2$

Given that $f(x)+f(y) = f[x \times \sqrt{1-y^2}+ y\times \sqrt{1-x^2}]$ To prove $f(4x^3-3x) + 3f(x) = 0$

$ |f(x) - f(y)| \le 7| x-y |^{201} $ I need to find a linear relation between $f(101)$ and $f(200)$

Verify surjectivity of the function $f$ satisfying: $f(x)+f(x^2)=x$

How to interpret the functional identity $f(a+b)=f(a)+f(b)$?

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