Question

Find $f(x)$ for which: $f(x^4+2x^2+2)-1=(f(x)-1)^4+4x(f(x)-1)^2+4x^2$

score 96 · Answer 1 · 2017-08-21 05:41:52

96

Views

Find $f(x)$ for which: $f(x^4+2x^2+2)-1=(f(x)-1)^4+4x(f(x)-1)^2+4x^2$

Published on 21 Aug 2017 - 5:41

score 88 · Answer 2 · 2017-08-21 16:44:21

88

Views

Cauchy's functional equation $f (x+y)=f (x)+f(y)$ in subdomains

Published on 21 Aug 2017 - 16:44

score 49 · Answer 3 · 2017-08-21 21:23:04

49

Views

Let $F$ be a function with domain $\mathbb Z^+$ such that $F(1)+F(2)+F(3)+......F(n)=n^2F(n)$. If $F(1)=2006$, then find the value of $F(2005)$

Published on 21 Aug 2017 - 21:23

score 215 · Answer 4 · 2017-08-22 04:20:08

215

Views

A multiplicative functional equation

Published on 22 Aug 2017 - 4:20

score 72 · Answer 5 · 2017-08-22 13:37:46

72

Views

What are some things to keep in mind while finding out domain and range of a function?

Published on 22 Aug 2017 - 13:37

score 197 · Answer 6 · 2017-08-22 14:54:17

197

Views

What exactly do we call a linear equation?

Published on 22 Aug 2017 - 14:54

score 108 · Answer 7 · 2017-08-23 03:31:59

108

Views

By which assumptions on $g$ could we solve the functional equation $f\circ f=g$?

Published on 23 Aug 2017 - 3:31

score 52 · Answer 8 · 2017-08-23 08:32:51

52

Views

Does local additivity imply local linearity?

Published on 23 Aug 2017 - 8:32

score 107 · Answer 9 · 2017-08-24 16:09:22

107

Views

Solving an equation with a function

Published on 24 Aug 2017 - 16:09

score 124 · Answer 10 · 2026-04-06 07:38:23

124

Views

Solve functional equation: $\frac{F(x)}{F(1)} = 2F\left(\frac{(1+x)^2}{4a}\right)-F(x/a)$

Published on 06 Apr 2026 - 7:38

score 437 · Answer 11 · 2017-08-26 02:06:09

437

Views

How to solve the iterated function $f(f(x))=x^2+x$?

Published on 26 Aug 2017 - 2:06

score 1.3k · Answer 12 · 2017-08-26 02:31:24

1.3k

Views

How to solve the functional equation $f(2x)=2f(x)/(1+(f(x))^2)$

Published on 26 Aug 2017 - 2:31

score 1.2k · Answer 13 · 2017-08-26 22:00:18

1.2k

Views

Find all the functions $f: \mathbb{N} \to \mathbb{N} $ such that $(m+f(n))(n+f(m))$ is a perfect square for all $m,n$

Published on 26 Aug 2017 - 22:00

score 135 · Answer 14 · 2026-03-29 17:11:49

135

Views

Find all the functions satisfying $\lvert f(x + iy) \rvert = \lvert f(x) + f(iy) \rvert$

Published on 29 Mar 2026 - 17:11

score 230 · Answer 15 · 2017-08-31 17:23:38

Reducing $2f\left(\frac{x+2y}{2}\right)+2f\left(\frac{x-2y}{2}\right)=f(x)+4f(y)$ to the quadratic functional equation

List Question

Find $f(x)$ for which: $f(x^4+2x^2+2)-1=(f(x)-1)^4+4x(f(x)-1)^2+4x^2$

Cauchy's functional equation $f (x+y)=f (x)+f(y)$ in subdomains

Let $F$ be a function with domain $\mathbb Z^+$ such that $F(1)+F(2)+F(3)+......F(n)=n^2F(n)$. If $F(1)=2006$, then find the value of $F(2005)$

A multiplicative functional equation

What are some things to keep in mind while finding out domain and range of a function?

What exactly do we call a linear equation?

By which assumptions on $g$ could we solve the functional equation $f\circ f=g$?

Does local additivity imply local linearity?

Solving an equation with a function

Solve functional equation: $\frac{F(x)}{F(1)} = 2F\left(\frac{(1+x)^2}{4a}\right)-F(x/a)$

How to solve the iterated function $f(f(x))=x^2+x$?

How to solve the functional equation $f(2x)=2f(x)/(1+(f(x))^2)$

Find all the functions $f: \mathbb{N} \to \mathbb{N} $ such that $(m+f(n))(n+f(m))$ is a perfect square for all $m,n$

Find all the functions satisfying $\lvert f(x + iy) \rvert = \lvert f(x) + f(iy) \rvert$

Reducing $2f\left(\frac{x+2y}{2}\right)+2f\left(\frac{x-2y}{2}\right)=f(x)+4f(y)$ to the quadratic functional equation

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