List questions from functional-equations

Published on 30 Sep 2015 - 5:23

153

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Let $f:\mathbb R\rightarrow \mathbb R$ be a continuous function such that $f(x)-2f(\frac{x}{2})+f(\frac{x}{4})=x^{2}$ . Then $f(3)$ =?

Published on 30 Sep 2015 - 10:36

87

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Functional equation $f(h(y)x+y)=g(y)f(x)$

Published on 01 Oct 2015 - 9:28

336

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if I know $f(x+1) = 2f(x) + 1$, how do I solve f(x)

Published on 29 Mar 2026 - 9:11

197

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Is there a function satisfying the following properties $ f^{n}(x)=(f(x))^{n+1}$??

Published on 03 Oct 2015 - 15:11

250

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Finding the "hidden values".

Published on 03 Oct 2015 - 15:19

66

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Find the function $f(x)$

Published on 06 Oct 2015 - 3:19

344

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A function that is zero for every integer multiple of $k$

Published on 01 Apr 2026 - 17:52

83

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What "natural" functions besides $g(x) = x$ and $g(x) =\dfrac{c^{x}}{c^{x}+c^{1/2}} $ satisfy $g(x)+g(1-x) = 1$?

Published on 12 Oct 2015 - 4:36

442

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For which polynomials $P$ does there exist a polynomial $Q$ such that $P(x)=Q(x)Q'(x)$?

Published on 12 Oct 2015 - 18:56

205

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How can I find $f'(2x)$ given that $xf(x)-yf(y)=(x-y)f(x+y)$?

Published on 20 Mar 2026 - 15:29

38

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Two variable equation, weighting of stock

Published on 31 Mar 2026 - 0:18

485

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Vector Space Structures over ($\mathbb{R}$,+)

Published on 01 Apr 2026 - 1:19

106

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$F(F(x)+x)^k)=(F(x)+x)^2-x$

Published on 01 Apr 2026 - 0:57

86

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Monotonically increasing functions 123

Published on 29 Mar 2026 - 4:26

List Question

Solving functional equation $2f(x) = f(2x)$

Let $f:\mathbb R\rightarrow \mathbb R$ be a continuous function such that $f(x)-2f(\frac{x}{2})+f(\frac{x}{4})=x^{2}$ . Then $f(3)$ =?

Functional equation $f(h(y)x+y)=g(y)f(x)$

if I know $f(x+1) = 2f(x) + 1$, how do I solve f(x)

Is there a function satisfying the following properties $ f^{n}(x)=(f(x))^{n+1}$??

Finding the "hidden values".

Find the function $f(x)$

A function that is zero for every integer multiple of $k$

What "natural" functions besides $g(x) = x$ and $g(x) =\dfrac{c^{x}}{c^{x}+c^{1/2}} $ satisfy $g(x)+g(1-x) = 1$?

For which polynomials $P$ does there exist a polynomial $Q$ such that $P(x)=Q(x)Q'(x)$?

How can I find $f'(2x)$ given that $xf(x)-yf(y)=(x-y)f(x+y)$?

Two variable equation, weighting of stock

Vector Space Structures over ($\mathbb{R}$,+)

$F(F(x)+x)^k)=(F(x)+x)^2-x$

Monotonically increasing functions 123

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