Question

Can someone guide me through this functional equation?

score 78 · Answer 1 · 2019-07-13 20:21:04

78

Views

Can someone guide me through this functional equation?

Published on 13 Jul 2019 - 20:21

score 127 · Answer 2 · 2019-07-15 01:54:10

127

Views

Are there any smooth/analytic solutions to the functional equation $f(x+1)-f(x)=f\left(\frac 1x\right)$?

Published on 15 Jul 2019 - 1:54

score 106 · Answer 3 · 2019-07-15 02:41:39

106

Views

Given $a,b,c$ positive numbers, is there a function $h$ such that $h(ax+b) = c \cdot h(x)$ for all $x>0$?

Published on 15 Jul 2019 - 2:41

score 87 · Answer 4 · 2026-03-26 16:06:27

87

Views

show this function have this $2f(\sqrt{xy})=f(x)+f(y),\forall x,y>0$

Published on 26 Mar 2026 - 16:06

score 1.3k · Answer 5 · 2019-07-18 02:26:20

1.3k

Views

(Olympiad Question) $f(2x) + 2f(y) = f(f(x+y))$

Published on 18 Jul 2019 - 2:26

score 69 · Answer 6 · 2026-03-25 00:23:36

69

Views

Iterative functional equation $f \circ f = f$

Published on 25 Mar 2026 - 0:23

score 132 · Answer 7 · 2019-07-19 23:29:56

132

Views

Is there a continuous function $f$ satisfying $f(x)^2=f\left(x^2\right)$, $f(0)=1$ and $ f(1)=0$?

Published on 19 Jul 2019 - 23:29

score 85 · Answer 8 · 2019-07-20 18:25:51

85

Views

Find all functions $f: \mathbb{R} \rightarrow \mathbb {R}$ such that $f(x+y)+f(x-y)=2f(x)\cos y$

Published on 20 Jul 2019 - 18:25

score 99 · Answer 9 · 2019-07-20 19:46:23

99

Views

Problem involving the functional equation $ f(y+x)-f(y-x)= 2xf'(y) $

Published on 20 Jul 2019 - 19:46

score 123 · Answer 10 · 2026-03-27 08:42:57

123

Views

Non-exponential functions satisfying $f(ab) = f(a) + f(b)$

Published on 27 Mar 2026 - 8:42

score 121 · Answer 11 · 2019-07-22 12:34:15

121

Views

Problem with existence of discontinuous additive function.

Published on 22 Jul 2019 - 12:34

score 258 · Answer 12 · 2019-07-22 15:00:48

258

Views

Characterizing the solutions of the functional equation $ f ( 3 x ) - f ( 2 x ) = f ( 2 x ) - f ( x ) $

Published on 22 Jul 2019 - 15:00

score 75 · Answer 13 · 2019-07-22 20:26:02

75

Views

Given $a$ and $c$ positive numbers, is there a function $h$ such that $h(-ax)= -ch(x)$ for all $x$?

Published on 22 Jul 2019 - 20:26

score 53 · Answer 14 · 2019-07-23 04:09:13

53

Views

How can I attempt this FE

Published on 23 Jul 2019 - 4:09

score 148 · Answer 15 · 2019-07-25 12:00:10

148

Views

Are $f$ satisfying $|f(y)| = |f(x+y) - f(x)|$ additive?

Published on 25 Jul 2019 - 12:00

List Question

Can someone guide me through this functional equation?

Are there any smooth/analytic solutions to the functional equation $f(x+1)-f(x)=f\left(\frac 1x\right)$?

Given $a,b,c$ positive numbers, is there a function $h$ such that $h(ax+b) = c \cdot h(x)$ for all $x>0$?

show this function have this $2f(\sqrt{xy})=f(x)+f(y),\forall x,y>0$

(Olympiad Question) $f(2x) + 2f(y) = f(f(x+y))$

Iterative functional equation $f \circ f = f$

Is there a continuous function $f$ satisfying $f(x)^2=f\left(x^2\right)$, $f(0)=1$ and $ f(1)=0$?

Find all functions $f: \mathbb{R} \rightarrow \mathbb {R}$ such that $f(x+y)+f(x-y)=2f(x)\cos y$

Problem involving the functional equation $ f(y+x)-f(y-x)= 2xf'(y) $

Non-exponential functions satisfying $f(ab) = f(a) + f(b)$

Problem with existence of discontinuous additive function.

Characterizing the solutions of the functional equation $ f ( 3 x ) - f ( 2 x ) = f ( 2 x ) - f ( x ) $

Given $a$ and $c$ positive numbers, is there a function $h$ such that $h(-ax)= -ch(x)$ for all $x$?

How can I attempt this FE

Are $f$ satisfying $|f(y)| = |f(x+y) - f(x)|$ additive?

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