Question

Is every function with this property an exponential function.

score 65 · Answer 1 · 2020-04-28 20:19:30

65

Views

Is every function with this property an exponential function.

Published on 28 Apr 2020 - 20:19

score 78 · Answer 2 · 2026-03-29 05:49:44

78

Views

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

Published on 29 Mar 2026 - 5:49

score 190 · Answer 3 · 2026-03-25 15:53:39

190

Views

Solving $f(x+1)=xf(x)f\left(\frac1x\right)$

Published on 25 Mar 2026 - 15:53

score 95 · Answer 4 · 2020-04-30 08:27:15

95

Views

Is the existence of a doubling time characteristic for exponential growth

Published on 30 Apr 2020 - 8:27

score 86 · Answer 5 · 2020-04-30 09:43:52

86

Views

If a function is additive on the interval $(-1/3, 1/3)$ does it follow it is linear?

Published on 30 Apr 2020 - 9:43

score 29 · Answer 6 · 2026-03-26 17:33:04

29

Views

How can I determine functions satisfying the following conditions?

Published on 26 Mar 2026 - 17:33

score 184 · Answer 7 · 2020-05-01 10:03:58

184

Views

Finding $f$ such that $f(x+\frac1y)+f(y+\frac1z)+f(z+\frac1x)=1$ for positive $x$, $y$, $z$ with $xyz=1$. Explain existing answer.

Published on 01 May 2020 - 10:03

score 96 · Answer 8 · 2026-02-24 14:24:53

96

Views

Quadratic Recurrence $a_{n+1} = 4a_n - 4a_n^2$

Published on 24 Feb 2026 - 14:24

score 190 · Answer 9 · 2020-05-02 15:13:01

190

Views

Solving the functional equation $f\big(xf(y)-y\big)+f(xy-x)+f(x+y)=2xy$

Published on 02 May 2020 - 15:13

score 94 · Answer 10 · 2026-02-24 14:28:20

94

Views

Let $f : \mathbb R^+ \rightarrow \mathbb R^+$ satisfies $f(f(x)) + f(x) = 6x$. Show that $f(x) = 2x$ only.

Published on 24 Feb 2026 - 14:28

score 118 · Answer 11 · 2020-05-03 09:30:09

118

Views

$3f(2x + 1) = f(x) + 5x$. Find continuous $f$.

Published on 03 May 2020 - 9:30

score 220 · Answer 12 · 2020-05-04 10:58:13

220

Views

If continuity condition is necessary for Miklós Schweitzer 2015 Problem 8

Published on 04 May 2020 - 10:58

score 62 · Answer 13 · 2020-05-05 01:37:31

62

Views

Functional equation: $ f : \mathbb R ^ * \to \mathbb R $ with $ \frac 1 x f ( - x ) + f \left( \frac 1 x \right) = x $

Published on 05 May 2020 - 1:37

score 95 · Answer 14 · 2020-05-05 03:20:27

95

Views

A solution to the functional equation $ f(xy) = f(x) + f(y) + \frac{x+y-1}{xy} $

Published on 05 May 2020 - 3:20

score 110 · Answer 15 · 2020-05-05 06:58:37

110

Views

Continuous $f : \mathbb R \to \mathbb R$ satisfying $f\left(\sqrt{\frac{x^2 + y^2}{2}}\right) = \frac{f(x) + f(y)}{2}$

Published on 05 May 2020 - 6:58

List Question

Is every function with this property an exponential function.

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

Solving $f(x+1)=xf(x)f\left(\frac1x\right)$

Is the existence of a doubling time characteristic for exponential growth

If a function is additive on the interval $(-1/3, 1/3)$ does it follow it is linear?

How can I determine functions satisfying the following conditions?

Finding $f$ such that $f(x+\frac1y)+f(y+\frac1z)+f(z+\frac1x)=1$ for positive $x$, $y$, $z$ with $xyz=1$. Explain existing answer.

Quadratic Recurrence $a_{n+1} = 4a_n - 4a_n^2$

Solving the functional equation $f\big(xf(y)-y\big)+f(xy-x)+f(x+y)=2xy$

Let $f : \mathbb R^+ \rightarrow \mathbb R^+$ satisfies $f(f(x)) + f(x) = 6x$. Show that $f(x) = 2x$ only.

$3f(2x + 1) = f(x) + 5x$. Find continuous $f$.

If continuity condition is necessary for Miklós Schweitzer 2015 Problem 8

Functional equation: $ f : \mathbb R ^ * \to \mathbb R $ with $ \frac 1 x f ( - x ) + f \left( \frac 1 x \right) = x $

A solution to the functional equation $ f(xy) = f(x) + f(y) + \frac{x+y-1}{xy} $

Continuous $f : \mathbb R \to \mathbb R$ satisfying $f\left(\sqrt{\frac{x^2 + y^2}{2}}\right) = \frac{f(x) + f(y)}{2}$

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