Question

Functional Equation: $f(2x)=4^x f(x)^2f(x+1)^2$

score 181 · Answer 1 · 2017-08-12 21:31:32

181

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Functional Equation: $f(2x)=4^x f(x)^2f(x+1)^2$

Published on 12 Aug 2017 - 21:31

score 2.1k · Answer 2 · 2017-08-13 10:28:21

2.1k

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Find all strictly increasing functions on positive integers such that $f(f(n))=n+2$

Published on 13 Aug 2017 - 10:28

score 280 · Answer 3 · 2017-08-13 20:43:21

280

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Find all functions for $x+f(\frac1x) = 2f(x)$

Published on 13 Aug 2017 - 20:43

score 116 · Answer 4 · 2017-08-14 10:41:38

116

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$f(f(x)−y) = f(x)+f(f(y)−f(−x))+x$ find all functions

Published on 14 Aug 2017 - 10:41

score 518 · Answer 5 · 2017-08-14 23:51:26

518

Views

Interesting Functional Equations (Just for Fun)

Published on 14 Aug 2017 - 23:51

score 578 · Answer 6 · 2017-08-15 18:19:29

578

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Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$

Published on 15 Aug 2017 - 18:19

score 56 · Answer 7 · 2026-03-26 04:49:47

56

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Solving a functional equation between restriction of a function in an interval

Published on 26 Mar 2026 - 4:49

score 71 · Answer 8 · 2017-08-16 03:17:12

71

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How can I solve this functional equations

Published on 16 Aug 2017 - 3:17

score 1.9k · Answer 9 · 2017-08-16 12:30:04

1.9k

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Functional equation : $f(xf(y))=yf(x)$

Published on 16 Aug 2017 - 12:30

score 56 · Answer 10 · 2026-03-26 14:21:16

56

Views

Name for the invariant $f(x+c, y+c) = f(x,y)$?

Published on 26 Mar 2026 - 14:21

score 108 · Answer 11 · 2017-08-17 06:19:41

108

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Find all functions $g$ from the Real numbers itself, satisfying $g(x + y) + g(x)g(y) = g(xy) + g(x) + g(y)$

Published on 17 Aug 2017 - 6:19

score 142 · Answer 12 · 2017-08-17 10:57:37

142

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Is there any positive function $f$ such that $f(x)f(y)\leq |x-y|$ for every $x$ rational and $y$ irrational?

Published on 17 Aug 2017 - 10:57

score 864 · Answer 13 · 2017-08-18 04:59:42

864

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$f\left(\frac{2z}{1+z^2}\right)=\left(1+z^2\right)f(z)$, solve $f$.

Published on 18 Aug 2017 - 4:59

score 191 · Answer 14 · 2017-08-18 15:17:56

191

Views

Prove that $f$ is constant.

Published on 18 Aug 2017 - 15:17

score 204 · Answer 15 · 2017-08-19 09:19:18

204

Views

Functional equation : $ f(1)^3 + f(2)^3 + \ldots + f(n)^3 = (f(1) + f(2) + \ldots + f(n))^2$

Published on 19 Aug 2017 - 9:19

List Question

Functional Equation: $f(2x)=4^x f(x)^2f(x+1)^2$

Find all strictly increasing functions on positive integers such that $f(f(n))=n+2$

Find all functions for $x+f(\frac1x) = 2f(x)$

$f(f(x)−y) = f(x)+f(f(y)−f(−x))+x$ find all functions

Interesting Functional Equations (Just for Fun)

Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$

Solving a functional equation between restriction of a function in an interval

How can I solve this functional equations

Functional equation : $f(xf(y))=yf(x)$

Name for the invariant $f(x+c, y+c) = f(x,y)$?

Find all functions $g$ from the Real numbers itself, satisfying $g(x + y) + g(x)g(y) = g(xy) + g(x) + g(y)$

Is there any positive function $f$ such that $f(x)f(y)\leq |x-y|$ for every $x$ rational and $y$ irrational?

$f\left(\frac{2z}{1+z^2}\right)=\left(1+z^2\right)f(z)$, solve $f$.

Prove that $f$ is constant.

Functional equation : $ f(1)^3 + f(2)^3 + \ldots + f(n)^3 = (f(1) + f(2) + \ldots + f(n))^2$

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