List questions from functional-equations

Published on 23 Feb 2026 - 8:28

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Functional equation $f(n^2+1)-f(n^2)=1$

Published on 25 Jun 2023 - 7:28

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Prove that the function is injective

Published on 26 Jun 2023 - 10:46

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Prime factors of $k^2x^2+1$

Published on 27 Jun 2023 - 7:54

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Solutions to the functional equation $f'(x)=f(2x)$.

Published on 01 Jul 2023 - 14:51

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Finding the functions with given conditions.

Published on 01 Jul 2023 - 19:38

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Does function $f(x) = kf(x-a) + (1-k)f(x-b)$ for $a / b \notin \mathbb{Q}$ always have a limit?

Published on 06 Jul 2023 - 2:08

120

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Find $f(x)$ that satisfies the equation $f(x^2) + (f(x))^2 = 2x^2 - 2$

Published on 07 Jul 2023 - 16:22

32

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Finding values of other functions with the help of given function

Published on 08 Jul 2023 - 12:26

143

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Asymptotics for $f(x)$ such that $f(x) + f(x/2) + f(x/3) + f(x/4) + ... = x$?

Published on 26 Mar 2026 - 6:01

211

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Simple functional equation: $f(x)=f(y) \implies f(ax)=f(ay)$

Published on 13 Jul 2023 - 7:27

50

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Derivative of the energy functional

Published on 13 Jul 2023 - 9:29

120

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Solving the functional equation $f: (0,+\infty) \to (0, +\infty):$ $f(x) = f(f(f(x))+y) + f(xf(y))\times f(x+y)$

Published on 15 Jul 2023 - 8:48

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If $f : \mathbb{R} \to \mathbb{R}$ and $f(f(x))=x^2-x+1$, then find $f(2021)+f(1971)+f(50)$

Published on 17 Jul 2023 - 11:36

50

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Proving composite function properties

Published on 17 Jul 2023 - 13:18

List Question

$t(x) - t(x/2) + t(x/3) - t(x/4) + ... = 0$ implies $t(x) + t(x/2)+t(x/3)+t(x/4) = C x$?

Functional equation $f(n^2+1)-f(n^2)=1$

Prove that the function is injective

Prime factors of $k^2x^2+1$

Solutions to the functional equation $f'(x)=f(2x)$.

Finding the functions with given conditions.

Does function $f(x) = kf(x-a) + (1-k)f(x-b)$ for $a / b \notin \mathbb{Q}$ always have a limit?

Find $f(x)$ that satisfies the equation $f(x^2) + (f(x))^2 = 2x^2 - 2$

Finding values of other functions with the help of given function

Asymptotics for $f(x)$ such that $f(x) + f(x/2) + f(x/3) + f(x/4) + ... = x$?

Simple functional equation: $f(x)=f(y) \implies f(ax)=f(ay)$

Derivative of the energy functional

Solving the functional equation $f: (0,+\infty) \to (0, +\infty):$ $f(x) = f(f(f(x))+y) + f(xf(y))\times f(x+y)$

If $f : \mathbb{R} \to \mathbb{R}$ and $f(f(x))=x^2-x+1$, then find $f(2021)+f(1971)+f(50)$

Proving composite function properties

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