Question

$f(x + y)f(x − y) = ( f(x) + f(y) )^ 2− 4x^ 2 f(y)$ so why $f(2) \neq 2$?

score 52 · Answer 1 · 2014-05-02 17:11:56

52

Views

$f(x + y)f(x − y) = ( f(x) + f(y) )^ 2− 4x^ 2 f(y)$ so why $f(2) \neq 2$?

Published on 02 May 2014 - 17:11

score 578 · Answer 2 · 2014-05-03 21:58:58

578

Views

$f_{n+1}(x)=f_n(x+1)-f_n(x)$ functional equation and "classification of functions"

Published on 03 May 2014 - 21:58

score 600 · Answer 3 · 2014-05-03 23:48:19

600

Views

Tricky probability problem

Published on 03 May 2014 - 23:48

score 151 · Answer 4 · 2014-05-07 20:34:54

151

Views

Functional equation (is solution unique)

Published on 07 May 2014 - 20:34

score 96 · Answer 5 · 2014-05-09 05:26:06

96

Views

A problem about functional equations: $f\left(x^2+\frac14\right)=f(x)$

Published on 09 May 2014 - 5:26

score 233 · Answer 6 · 2014-05-10 15:34:12

233

Views

Solving the functional equation $f(x+y)-f(x)f(y)+g(x)g(y)=0$

Published on 10 May 2014 - 15:34

score 727 · Answer 7 · 2014-05-13 21:54:35

727

Views

Finding equations when given new center of a circle

Published on 13 May 2014 - 21:54

score 160 · Answer 8 · 2014-05-14 03:12:22

160

Views

Functional equation $f(x)=f(\sqrt{x})$

Published on 14 May 2014 - 3:12

score 292 · Answer 9 · 2014-05-14 07:11:48

292

Views

Continuous functions that satisfies $f(x) + f(1-x) + f(\sqrt{x^2+(1-x)}) = 0$ and $f(\frac12)=0$

Published on 14 May 2014 - 7:11

score 191 · Answer 10 · 2014-05-15 12:09:01

191

Views

Does a solution to this functional equation exist and if so can we construct it?

Published on 15 May 2014 - 12:09

score 74 · Answer 11 · 2014-05-15 20:15:13

74

Views

Can a linear solution make a non-linear (functional) differential equation linear?

Published on 15 May 2014 - 20:15

score 152 · Answer 12 · 2014-05-16 16:53:01

152

Views

Functional inequation on $\mathbb{R}$: $f\left(x+y^2\right)-f(x)\geq y$

Published on 16 May 2014 - 16:53

score 215 · Answer 13 · 2014-05-18 11:50:18

215

Views

If $f$ is not identically zero and $|f(x)| \le 1$ for $x$ $\in \mathbb{R}$, then also $|g(x)| \le 1$ for $x \in \mathbb{R}$

Published on 18 May 2014 - 11:50

score 5k · Answer 14 · 2014-05-19 16:08:22

5k

Views

If $f(3x)=f(x)$ and $f$ is continuous, show that $f(x)$ is a constant function.

Published on 19 May 2014 - 16:08

score 107 · Answer 15 · 2014-05-20 20:47:37

Proof that $\forall x \in \mathbb{R}, \forall n \in \mathbb{N}: (f(x))^n = f(nx)$ only has solutions of the form $f(x) = c^x$ for some constant $c$

List Question

$f(x + y)f(x − y) = ( f(x) + f(y) )^ 2− 4x^ 2 f(y)$ so why $f(2) \neq 2$?

$f_{n+1}(x)=f_n(x+1)-f_n(x)$ functional equation and "classification of functions"

Tricky probability problem

Functional equation (is solution unique)

A problem about functional equations: $f\left(x^2+\frac14\right)=f(x)$

Solving the functional equation $f(x+y)-f(x)f(y)+g(x)g(y)=0$

Finding equations when given new center of a circle

Functional equation $f(x)=f(\sqrt{x})$

Continuous functions that satisfies $f(x) + f(1-x) + f(\sqrt{x^2+(1-x)}) = 0$ and $f(\frac12)=0$

Does a solution to this functional equation exist and if so can we construct it?

Can a linear solution make a non-linear (functional) differential equation linear?

Functional inequation on $\mathbb{R}$: $f\left(x+y^2\right)-f(x)\geq y$

If $f$ is not identically zero and $|f(x)| \le 1$ for $x$ $\in \mathbb{R}$, then also $|g(x)| \le 1$ for $x \in \mathbb{R}$

If $f(3x)=f(x)$ and $f$ is continuous, show that $f(x)$ is a constant function.

Proof that $\forall x \in \mathbb{R}, \forall n \in \mathbb{N}: (f(x))^n = f(nx)$ only has solutions of the form $f(x) = c^x$ for some constant $c$

Trending Questions

Popular # Hahtags

Popular Questions