Question

Find all functions $f:\mathbb R \rightarrow \mathbb R$ such that $f (x+xy+f(y) )= (f(x)+ \frac 12 )\ (f(y)+ \frac 12 \ ).$

score 305 · Answer 1 · 2016-02-10 15:17:55

Find all functions $f:\mathbb R \rightarrow \mathbb R$ such that $f (x+xy+f(y) )= (f(x)+ \frac 12 )\ (f(y)+ \frac 12 \ ).$

score 163 · Answer 2 · 2016-02-14 08:11:35

163

Views

Is this graph plot for real?

Published on 14 Feb 2016 - 8:11

score 4.8k · Answer 3 · 2016-02-15 09:31:29

4.8k

Views

If $f:[0,\infty)\to [0,\infty)$ and $f(x+y)=f(x)+f(y)$ then prove that $f(x)=ax$

Published on 15 Feb 2016 - 9:31

score 281 · Answer 4 · 2016-02-15 20:41:25

281

Views

Is the function from the Cauchy functional equation, $f(x+y)=f(x)+f(y)$ injective?

Published on 15 Feb 2016 - 20:41

score 146 · Answer 5 · 2016-02-17 16:12:26

146

Views

Find all functions $f:\mathbb R\to \mathbb R$ such that $f(a^2+b^2)=f(a^2-b^2)+f(2ab)$ for every real $a$,$b$

Published on 17 Feb 2016 - 16:12

score 144 · Answer 6 · 2016-02-20 13:16:26

144

Views

Find all real and continuous functions that are a 3-involution.

Published on 20 Feb 2016 - 13:16

score 127 · Answer 7 · 2016-02-21 14:47:04

127

Views

Find $f(x)$ if for every $x$: $f(x) + f(\frac {2x-3}{x-1}) = x$

Published on 21 Feb 2016 - 14:47

score 261 · Answer 8 · 2016-02-23 10:57:31

261

Views

Prove that $f(x)=8$ for all natural numbers $x\ge{8}$

Published on 23 Feb 2016 - 10:57

score 578 · Answer 9 · 2016-02-23 19:19:10

578

Views

The function $f (x) = f \left (\frac x2 \right ) + f \left (\frac x2 + \frac 12\right)$

Published on 23 Feb 2016 - 19:19

score 921 · Answer 10 · 2016-02-24 16:30:58

921

Views

To find whether $f:\mathbb{N}\to\mathbb{N}$ defined with $f(x)=\left\lfloor\frac{x+1}{2}\right\rfloor$ is one-one and onto

Published on 24 Feb 2016 - 16:30

score 38 · Answer 11 · 2016-02-25 14:58:45

38

Views

Find the equation of the common part of two objects

Published on 25 Feb 2016 - 14:58

score 37 · Answer 12 · 2016-02-25 15:44:08

37

Views

Finding a possible region where this PDE has a solution

Published on 25 Feb 2016 - 15:44

score 80 · Answer 13 · 2016-02-26 21:20:26

80

Views

How to solve $2f(x)+xf(\frac{1}{x})-2f(|\sqrt2 \sin(\pi(x+\frac{1}{4}))|) = 4 \cos^2 \frac{\pi x}{2}+x\cos\frac{\pi}{x}$

Published on 26 Feb 2016 - 21:20

score 3.6k · Answer 14 · 2016-03-01 20:22:38

3.6k

Views

What does non-degenerate mean?

Published on 01 Mar 2016 - 20:22

score 1.7k · Answer 15 · 2026-03-30 03:53:46

1.7k

Views

Can a conformal map be turned into an isometry?

Published on 30 Mar 2026 - 3:53

List Question

Find all functions $f:\mathbb R \rightarrow \mathbb R$ such that $f (x+xy+f(y) )= (f(x)+ \frac 12 )\ (f(y)+ \frac 12 \ ).$

Is this graph plot for real?

If $f:[0,\infty)\to [0,\infty)$ and $f(x+y)=f(x)+f(y)$ then prove that $f(x)=ax$

Is the function from the Cauchy functional equation, $f(x+y)=f(x)+f(y)$ injective?

Find all functions $f:\mathbb R\to \mathbb R$ such that $f(a^2+b^2)=f(a^2-b^2)+f(2ab)$ for every real $a$,$b$

Find all real and continuous functions that are a 3-involution.

Find $f(x)$ if for every $x$: $f(x) + f(\frac {2x-3}{x-1}) = x$

Prove that $f(x)=8$ for all natural numbers $x\ge{8}$

The function $f (x) = f \left (\frac x2 \right ) + f \left (\frac x2 + \frac 12\right)$

To find whether $f:\mathbb{N}\to\mathbb{N}$ defined with $f(x)=\left\lfloor\frac{x+1}{2}\right\rfloor$ is one-one and onto

Find the equation of the common part of two objects

Finding a possible region where this PDE has a solution

How to solve $2f(x)+xf(\frac{1}{x})-2f(|\sqrt2 \sin(\pi(x+\frac{1}{4}))|) = 4 \cos^2 \frac{\pi x}{2}+x\cos\frac{\pi}{x}$

What does non-degenerate mean?

Can a conformal map be turned into an isometry?

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