Question

if $2f\left(\frac{x}{x^2+x+1}\right)=\frac{x^2}{x^4+x^2+1}$ then what is $f(x)$?

score 77 · Answer 1 · 2015-11-27 10:35:39

77

Views

if $2f\left(\frac{x}{x^2+x+1}\right)=\frac{x^2}{x^4+x^2+1}$ then what is $f(x)$?

Published on 27 Nov 2015 - 10:35

score 54 · Answer 2 · 2015-11-27 18:12:23

54

Views

Does the equation $f(x)+g(y)=x^2+xy+y^2$ have solutions in real functions $f$ and $g$?

Published on 27 Nov 2015 - 18:12

score 82 · Answer 3 · 2015-11-28 22:46:19

82

Views

continuous function and functional equation

Published on 28 Nov 2015 - 22:46

score 322 · Answer 4 · 2015-11-28 23:44:11

322

Views

Finding $f(n)=f(f(n-1))+f(f(n+1))$

Published on 28 Nov 2015 - 23:44

score 89 · Answer 5 · 2015-11-29 16:02:39

89

Views

Prove that functional equation doesn't have range $\Bbb R.$

Published on 29 Nov 2015 - 16:02

score 150 · Answer 6 · 2015-11-29 17:08:06

150

Views

Functions satisfying the functional equation $ \big( 1 - f ( x ) f ( y ) \big) f ( x + y ) = f ( x ) + f ( y ) $

Published on 29 Nov 2015 - 17:08

score 139 · Answer 7 · 2015-11-30 13:20:42

139

Views

Solution of the functional equation $g(x)g(z) = g(x+z)+g(x-z)$

Published on 30 Nov 2015 - 13:20

score 1.2k · Answer 8 · 2026-04-04 09:54:50

1.2k

Views

Giving tight asymptotic bounds for $ T ( n ) = T \left( \frac n { \log n } \right) + \log \log n $

Published on 04 Apr 2026 - 9:54

score 3.4k · Answer 9 · 2015-12-01 13:04:31

3.4k

Views

Differentiability of $f(x+y) = f(x)f(y)$

Published on 01 Dec 2015 - 13:04

score 335 · Answer 10 · 2015-12-02 12:20:59

335

Views

Functional equation $f(x+y)-f(x)-f(y)=\alpha\big(f(xy)-f(x)f(y)\big)$ is solvable without regularity conditions

Published on 02 Dec 2015 - 12:20

score 206 · Answer 11 · 2015-12-03 12:18:03

206

Views

Functional Equation $f(m + f(n)) = f(m) - n$

Published on 03 Dec 2015 - 12:18

score 72 · Answer 12 · 2015-12-05 12:45:31

72

Views

Is it possible to compute $\Gamma(\rho_k)$ or $\zeta(3+2\omega_k)$, when $\rho_k=\frac{1}{2}+i\omega_k$ is a nontrivial zero of Riemann zeta function?

Published on 05 Dec 2015 - 12:45

score 255 · Answer 13 · 2015-12-06 02:36:17

255

Views

Does induction find all solutions?

Published on 06 Dec 2015 - 2:36

score 154 · Answer 14 · 2015-12-07 09:25:40

154

Views

Functional equation $f\left(\frac{1}{x}\right)+(x+1)f(x)=1$

Published on 07 Dec 2015 - 9:25

score 70 · Answer 15 · 2015-12-08 06:55:51

70

Views

Functional Equation similar to Cauchy's: $\{f(x)\}+\{f(y)\}=\{f(x+y)\}$

Published on 08 Dec 2015 - 6:55

List Question

if $2f\left(\frac{x}{x^2+x+1}\right)=\frac{x^2}{x^4+x^2+1}$ then what is $f(x)$?

Does the equation $f(x)+g(y)=x^2+xy+y^2$ have solutions in real functions $f$ and $g$?

continuous function and functional equation

Finding $f(n)=f(f(n-1))+f(f(n+1))$

Prove that functional equation doesn't have range $\Bbb R.$

Functions satisfying the functional equation $ \big( 1 - f ( x ) f ( y ) \big) f ( x + y ) = f ( x ) + f ( y ) $

Solution of the functional equation $g(x)g(z) = g(x+z)+g(x-z)$

Giving tight asymptotic bounds for $ T ( n ) = T \left( \frac n { \log n } \right) + \log \log n $

Differentiability of $f(x+y) = f(x)f(y)$

Functional equation $f(x+y)-f(x)-f(y)=\alpha\big(f(xy)-f(x)f(y)\big)$ is solvable without regularity conditions

Functional Equation $f(m + f(n)) = f(m) - n$

Is it possible to compute $\Gamma(\rho_k)$ or $\zeta(3+2\omega_k)$, when $\rho_k=\frac{1}{2}+i\omega_k$ is a nontrivial zero of Riemann zeta function?

Does induction find all solutions?

Functional equation $f\left(\frac{1}{x}\right)+(x+1)f(x)=1$

Functional Equation similar to Cauchy's: $\{f(x)\}+\{f(y)\}=\{f(x+y)\}$

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