Question

Solving simple functional relation

score 32 · Answer 1 · 2020-07-20 21:07:47

32

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Solving simple functional relation

Published on 20 Jul 2020 - 21:07

score 76 · Answer 2 · 2026-03-26 06:42:46

76

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Show that the following power series satisfies this functional equation $f\left(\frac{2x}{1+x^2}\right)=(1+x^2)\,f(x)$.

Published on 26 Mar 2026 - 6:42

score 57 · Answer 3 · 2020-07-21 15:58:50

57

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Function satisfying some constraints

Published on 21 Jul 2020 - 15:58

score 65 · Answer 4 · 2020-07-22 04:40:21

65

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Functional Equation in the rationals: $f(xy)=f(x)f(y)-f(x+y)+1$

Published on 22 Jul 2020 - 4:40

score 546 · Answer 5 · 2020-07-22 11:51:18

546

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Find all functions $f:\mathbb{R}^+\to \mathbb{R}$ such that $xf(xf(x)-4)-1=4x$

Published on 22 Jul 2020 - 11:51

score 186 · Answer 6 · 2020-07-23 20:28:21

186

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If $f(2n)=\frac1{f(n)+1}$ and $f(2n+1)=f(n)+1$ for all $n\in\Bbb N$, then find $n$ such that $f(n)=14/5$.

Published on 23 Jul 2020 - 20:28

score 121 · Answer 7 · 2020-07-25 19:50:41

Find all functions $f:\Bbb R^+\to\Bbb R^+$ s.t. for all $x\in \Bbb R^+$ the following is valid: $f\bigg(\frac{1}{f(x)}\bigg)=\frac{1}{x}$

score 129 · Answer 8 · 2020-07-26 02:03:20

129

Views

Polynomial in two variables such that $P(x,y)=P(x+y,x-y)$

Published on 26 Jul 2020 - 2:03

score 112 · Answer 9 · 2020-07-26 14:40:15

112

Views

What is a solution to the recurrence relation $f(n) = f(n-1) +f\Big(\left\lfloor \frac{n}{2} \right\rfloor\Big)$?

Published on 26 Jul 2020 - 14:40

score 68 · Answer 10 · 2020-07-26 23:05:15

68

Views

Solve a power tower of function compositions

Published on 26 Jul 2020 - 23:05

score 103 · Answer 11 · 2026-03-30 18:12:04

103

Views

How does WolframAlpha solve this recursion?

Published on 30 Mar 2026 - 18:12

score 102 · Answer 12 · 2020-07-28 15:35:54

Functional equations on $ \mathbb Q ^ + $: $ f ( x + 1 ) = f ( x ) + 1 $ and $ f \left( x ^ 2 \right) = f ^ 2 ( x ) $

score 859 · Answer 13 · 2016-07-05 18:53:01

859

Views

Function that is both midpoint convex and concave: $f\left(\frac{x+y}{2}\right) = \frac{f(x)+f(y)}{2}$

Published on 05 Jul 2016 - 18:53

score 1.1k · Answer 14 · 2016-07-06 07:17:17

1.1k

Views

Find $f(5)$ where $f$ satisfies $f(x)+f(1/(1-x))=x $

Published on 06 Jul 2016 - 7:17

score 722 · Answer 15 · 2016-07-06 09:04:01

722

Views

The function $f$ has property: $f(x)+f(1/x)=x$ and what is the largest set of real numbers?

Published on 06 Jul 2016 - 9:04

List Question

Solving simple functional relation

Show that the following power series satisfies this functional equation $f\left(\frac{2x}{1+x^2}\right)=(1+x^2)\,f(x)$.

Function satisfying some constraints

Functional Equation in the rationals: $f(xy)=f(x)f(y)-f(x+y)+1$

Find all functions $f:\mathbb{R}^+\to \mathbb{R}$ such that $xf(xf(x)-4)-1=4x$

If $f(2n)=\frac1{f(n)+1}$ and $f(2n+1)=f(n)+1$ for all $n\in\Bbb N$, then find $n$ such that $f(n)=14/5$.

Find all functions $f:\Bbb R^+\to\Bbb R^+$ s.t. for all $x\in \Bbb R^+$ the following is valid: $f\bigg(\frac{1}{f(x)}\bigg)=\frac{1}{x}$

Polynomial in two variables such that $P(x,y)=P(x+y,x-y)$

What is a solution to the recurrence relation $f(n) = f(n-1) +f\Big(\left\lfloor \frac{n}{2} \right\rfloor\Big)$?

Solve a power tower of function compositions

How does WolframAlpha solve this recursion?

Functional equations on $ \mathbb Q ^ + $: $ f ( x + 1 ) = f ( x ) + 1 $ and $ f \left( x ^ 2 \right) = f ^ 2 ( x ) $

Function that is both midpoint convex and concave: $f\left(\frac{x+y}{2}\right) = \frac{f(x)+f(y)}{2}$

Find $f(5)$ where $f$ satisfies $f(x)+f(1/(1-x))=x $

The function $f$ has property: $f(x)+f(1/x)=x$ and what is the largest set of real numbers?

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