Question

if $f(x)f(-x) = 0, \forall x \in\mathbb{R}$ can we prove that $f(x)=0, \forall x \in \mathbb{R}$

score 99 · Answer 1 · 2017-09-17 19:53:54

99

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if $f(x)f(-x) = 0, \forall x \in\mathbb{R}$ can we prove that $f(x)=0, \forall x \in \mathbb{R}$

Published on 17 Sep 2017 - 19:53

score 239 · Answer 2 · 2017-09-17 20:00:32

239

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Proving that $f(x+y) = f(x)+f(y) $ and $f(xy) = f(x)f(y)$ imply $f(x) = 0$ or $f(x) = x$

Published on 17 Sep 2017 - 20:00

score 116 · Answer 3 · 2017-09-19 01:56:52

116

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Multivariable calculus problem contest

Published on 19 Sep 2017 - 1:56

score 257 · Answer 4 · 2026-03-26 23:11:02

257

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$f ^{\prime \prime}(x) = f(x) f^{\prime \prime} (x-1) $

Published on 26 Mar 2026 - 23:11

score 42 · Answer 5 · 2017-09-20 14:31:52

42

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If $x_1, x_2, \cdots, x_n$ are the roots of $f(x)$, find the roots of $g(x)$

Published on 20 Sep 2017 - 14:31

score 47 · Answer 6 · 2017-09-20 16:13:08

47

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$g(x)=f(4^x,0)$, $f(a,b)=f(a+b,b-a)$. Show that $\exists$ a constant $c$ such that $g(x+c)=g(x)$ for all real $x$.

Published on 20 Sep 2017 - 16:13

score 49 · Answer 7 · 2017-09-21 14:14:36

49

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Functional Relationships

Published on 21 Sep 2017 - 14:14

score 840 · Answer 8 · 2017-09-23 00:18:10

840

Views

Let $f(x) = \frac{7x+6}5$ and g$(x) = 10x+10$. Determine $(-10f+5g)(-4)$

Published on 23 Sep 2017 - 0:18

score 189 · Answer 9 · 2017-09-24 18:01:41

189

Views

How to solve functional equation?

Published on 24 Sep 2017 - 18:01

score 60 · Answer 10 · 2017-09-26 00:58:29

60

Views

Is there any analytical solution of this system of two linear inhomogeneous first-order PDE?

Published on 26 Sep 2017 - 0:58

score 184 · Answer 11 · 2017-09-26 09:21:08

184

Views

Has $f'(x)=f(x+1/2)$ non-oscillating solutions?

Published on 26 Sep 2017 - 9:21

score 159 · Answer 12 · 2017-09-26 11:48:37

159

Views

Functional equation which should have $f(x)=x$ as the unique solution

Published on 26 Sep 2017 - 11:48

score 96 · Answer 13 · 2026-03-29 22:27:51

96

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Determine this monotonic function

Published on 29 Mar 2026 - 22:27

score 111 · Answer 14 · 2017-09-27 13:01:25

111

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How can one solve this functional equation $f(u)f(v)=f(u+v)(f(u)+f(v)-(q+q^{-1}))+1$?

Published on 27 Sep 2017 - 13:01

score 244 · Answer 15 · 2026-04-02 04:38:49

244

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Functional equation: $f(2x)=f(x)+f^{-1}(x)$

Published on 02 Apr 2026 - 4:38

List Question

if $f(x)f(-x) = 0, \forall x \in\mathbb{R}$ can we prove that $f(x)=0, \forall x \in \mathbb{R}$

Proving that $f(x+y) = f(x)+f(y) $ and $f(xy) = f(x)f(y)$ imply $f(x) = 0$ or $f(x) = x$

Multivariable calculus problem contest

$f ^{\prime \prime}(x) = f(x) f^{\prime \prime} (x-1) $

If $x_1, x_2, \cdots, x_n$ are the roots of $f(x)$, find the roots of $g(x)$

$g(x)=f(4^x,0)$, $f(a,b)=f(a+b,b-a)$. Show that $\exists$ a constant $c$ such that $g(x+c)=g(x)$ for all real $x$.

Functional Relationships

Let $f(x) = \frac{7x+6}5$ and g$(x) = 10x+10$. Determine $(-10f+5g)(-4)$

How to solve functional equation?

Is there any analytical solution of this system of two linear inhomogeneous first-order PDE?

Has $f'(x)=f(x+1/2)$ non-oscillating solutions?

Functional equation which should have $f(x)=x$ as the unique solution

Determine this monotonic function

How can one solve this functional equation $f(u)f(v)=f(u+v)(f(u)+f(v)-(q+q^{-1}))+1$?

Functional equation: $f(2x)=f(x)+f^{-1}(x)$

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