Question

Limit involving iterated function $f_a(x)=x^2+a^2$

score 88 · Answer 1 · 2026-02-23 15:36:25

88

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Limit involving iterated function $f_a(x)=x^2+a^2$

Published on 23 Feb 2026 - 15:36

score 1k · Answer 2 · 2019-03-03 00:01:23

1k

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Let $g(z) = 1/(1+e^{-z})$ be the logistic function. Show that $1-g(z)=g(-z)$

Published on 03 Mar 2019 - 0:01

score 411 · Answer 3 · 2019-03-04 11:25:52

411

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Find $P(7/8)$ given ${P(5)}^2=P(6)$ and $(x-1)P(x+1)=(x+2)P(x)$

Published on 04 Mar 2019 - 11:25

score 288 · Answer 4 · 2026-03-25 20:39:45

288

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Euler-Lagrange equations for dependent multiple functions

Published on 25 Mar 2026 - 20:39

score 216 · Answer 5 · 2019-03-06 08:20:25

216

Views

A functional equation defined on the real axis.

Published on 06 Mar 2019 - 8:20

score 101 · Answer 6 · 2019-03-09 15:31:20

101

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find all fucntions such that $f(x+y) \geq f(x) + yf(f(x)) $

Published on 09 Mar 2019 - 15:31

score 268 · Answer 7 · 2019-03-11 23:42:14

268

Views

If $f(x) + f(2x)$ is continuous, is $f$ continuous or not?

Published on 11 Mar 2019 - 23:42

score 242 · Answer 8 · 2019-03-12 11:30:43

242

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Find all polynomials $P(x)$ with $P(x)P(1/x)=P(x)+P(1/x)$

Published on 12 Mar 2019 - 11:30

score 140 · Answer 9 · 2019-03-13 12:28:51

140

Views

$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant

Published on 13 Mar 2019 - 12:28

score 83 · Answer 10 · 2019-03-18 15:42:57

83

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Two functional equations

Published on 18 Mar 2019 - 15:42

score 65 · Answer 11 · 2019-03-20 14:09:55

65

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How to solve a functional equation involving log?

Published on 20 Mar 2019 - 14:09

score 1.3k · Answer 12 · 2019-03-21 05:25:09

1.3k

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Solving $f(yf(x)+x/y)=xyf(x^2+y^2)$ over the reals

Published on 21 Mar 2019 - 5:25

score 217 · Answer 13 · 2019-03-21 17:33:17

217

Views

Is there a solution to the functional equation $f(x)=2\log(x)^2f\left(x^\frac{3}{8}\right)^2f\left(x^\frac{1}{4}\right)^2$?

Published on 21 Mar 2019 - 17:33

score 168 · Answer 14 · 2019-03-22 03:51:55

168

Views

Find all f such that $f(f(y))+f(x-y)=f(xf(y)-x)$

Published on 22 Mar 2019 - 3:51

score 59 · Answer 15 · 2019-03-22 15:11:40

59

Views

$f:\mathbb{R} \to \mathbb{R}$ we have $f(b)-f(a)=(b-a)f'(\frac{a+b}{2})$ such function is polynomial of degree less than or equal to two.

Published on 22 Mar 2019 - 15:11

List Question

Limit involving iterated function $f_a(x)=x^2+a^2$

Let $g(z) = 1/(1+e^{-z})$ be the logistic function. Show that $1-g(z)=g(-z)$

Find $P(7/8)$ given ${P(5)}^2=P(6)$ and $(x-1)P(x+1)=(x+2)P(x)$

Euler-Lagrange equations for dependent multiple functions

A functional equation defined on the real axis.

find all fucntions such that $f(x+y) \geq f(x) + yf(f(x)) $

If $f(x) + f(2x)$ is continuous, is $f$ continuous or not?

Find all polynomials $P(x)$ with $P(x)P(1/x)=P(x)+P(1/x)$

$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant

Two functional equations

How to solve a functional equation involving log?

Solving $f(yf(x)+x/y)=xyf(x^2+y^2)$ over the reals

Is there a solution to the functional equation $f(x)=2\log(x)^2f\left(x^\frac{3}{8}\right)^2f\left(x^\frac{1}{4}\right)^2$?

Find all f such that $f(f(y))+f(x-y)=f(xf(y)-x)$

$f:\mathbb{R} \to \mathbb{R}$ we have $f(b)-f(a)=(b-a)f'(\frac{a+b}{2})$ such function is polynomial of degree less than or equal to two.

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