Question

What is the value $f(-4)$ in the under function such that $f(x)+f(\frac1x)=\frac{x^2-12x+1}{2x}.$

score 183 · Answer 1 · 2016-07-19 08:43:39

183

Views

What is the value $f(-4)$ in the under function such that $f(x)+f(\frac1x)=\frac{x^2-12x+1}{2x}.$

Published on 19 Jul 2016 - 8:43

score 103 · Answer 2 · 2026-03-29 03:28:24

103

Views

Does there exist a multiplicative $f:\mathbb{Q}^+\to\mathbb{Q}^+$ such that $f\neq x\mapsto x^a$ for all $a$?

Published on 29 Mar 2026 - 3:28

score 164 · Answer 3 · 2016-07-20 18:51:22

164

Views

The Bi-linear Functional Equation $\sum_{i=1}^{n}f_i(x)g_i(y)=0$

Published on 20 Jul 2016 - 18:51

score 500 · Answer 4 · 2016-07-22 18:42:41

500

Views

Find all solutions to $f\left(x^2+xf(y)\right)=xf(x+y)$

Published on 22 Jul 2016 - 18:42

score 51 · Answer 5 · 2026-03-27 13:20:08

51

Views

Sequence of compact operators that converges to a bounded linear operator $K_{\lambda}$

Published on 27 Mar 2026 - 13:20

score 106 · Answer 6 · 2016-07-24 12:31:05

106

Views

Find all functions such that $f(c+x)+f(c-x)=k$ for some constants $c,k$

Published on 24 Jul 2016 - 12:31

score 234 · Answer 7 · 2016-07-24 21:08:37

234

Views

Function with $f(f(n))=f(n-1)f(n+1)-f(n)^2$

Published on 24 Jul 2016 - 21:08

score 1.9k · Answer 8 · 2016-07-26 06:35:41

1.9k

Views

If $f$ is a function defined for all real $x$ and satisfies $f(x+y) = f(x) + f(y) + xy(x+y)$, do $f'$ and $f''$ exist?

Published on 26 Jul 2016 - 6:35

score 290 · Answer 9 · 2016-07-26 12:36:44

290

Views

Does there exist any non-zero polynomial $f:\mathbb C \to \mathbb C$ such that $f(x+2)-2f(x+1)=f(x) , \forall x \in \mathbb C$?

Published on 26 Jul 2016 - 12:36

score 734 · Answer 10 · 2016-07-27 16:59:23

734

Views

Find all functions that satisfy $f(\frac{x+4}{1-x}) + f(x) = x$

Published on 27 Jul 2016 - 16:59

score 206 · Answer 11 · 2026-03-26 21:25:55

206

Views

Functional equation: $f(x)=x+\dfrac{f(2x)}{f(3x)}$

Published on 26 Mar 2026 - 21:25

score 373 · Answer 12 · 2016-07-31 13:49:03

373

Views

Find all functions on the non-zero reals to itself satisfying $f(xy)=f(x+y)(f(x)+f(y))$

Published on 31 Jul 2016 - 13:49

score 81 · Answer 13 · 2016-07-31 19:28:11

81

Views

Taking the same thing of both sides of an equation

Published on 31 Jul 2016 - 19:28

score 3.1k · Answer 14 · 2016-08-01 15:53:34

3.1k

Views

Find $f(x)$ if $f(x+y)=f(x)+f(y) - 2xy + (e^x -1)(e^y -1) $

Published on 01 Aug 2016 - 15:53

score 219 · Answer 15 · 2016-08-01 17:09:14

219

Views

$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$

Published on 01 Aug 2016 - 17:09

List Question

What is the value $f(-4)$ in the under function such that $f(x)+f(\frac1x)=\frac{x^2-12x+1}{2x}.$

Does there exist a multiplicative $f:\mathbb{Q}^+\to\mathbb{Q}^+$ such that $f\neq x\mapsto x^a$ for all $a$?

The Bi-linear Functional Equation $\sum_{i=1}^{n}f_i(x)g_i(y)=0$

Find all solutions to $f\left(x^2+xf(y)\right)=xf(x+y)$

Sequence of compact operators that converges to a bounded linear operator $K_{\lambda}$

Find all functions such that $f(c+x)+f(c-x)=k$ for some constants $c,k$

Function with $f(f(n))=f(n-1)f(n+1)-f(n)^2$

If $f$ is a function defined for all real $x$ and satisfies $f(x+y) = f(x) + f(y) + xy(x+y)$, do $f'$ and $f''$ exist?

Does there exist any non-zero polynomial $f:\mathbb C \to \mathbb C$ such that $f(x+2)-2f(x+1)=f(x) , \forall x \in \mathbb C$?

Find all functions that satisfy $f(\frac{x+4}{1-x}) + f(x) = x$

Functional equation: $f(x)=x+\dfrac{f(2x)}{f(3x)}$

Find all functions on the non-zero reals to itself satisfying $f(xy)=f(x+y)(f(x)+f(y))$

Taking the same thing of both sides of an equation

Find $f(x)$ if $f(x+y)=f(x)+f(y) - 2xy + (e^x -1)(e^y -1) $

$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$

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