List questions from functional-equations

Published on 25 Mar 2026 - 7:47

185

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Functional equation $f(x)-f(y)=\frac{1}{(x-y)^{2}}$

Published on 05 Nov 2014 - 14:35

83

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functional equation for $x^2$ $f(f(x))=x^4$

Published on 10 Nov 2014 - 11:22

516

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Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$

Published on 12 Nov 2014 - 15:24

1.8k

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A functional equation with no solution

Published on 12 Nov 2014 - 16:00

305

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About an integral equation

Published on 26 Mar 2026 - 6:19

99

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Find all odd functions $f: \mathbb{R} \to \mathbb{R}$ satisfying $f(t+1)=f(t)+1$ and $f\left(\frac{1}{t}\right)=\frac{1}{t^2}f(t)$

Published on 15 Nov 2014 - 15:04

273

Views

Find all polynomials with real coefficients that satisfy $(x^2-6x+8)P(x)=(x^2+2x)P(x-2)$

Published on 15 Nov 2014 - 17:31

132

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Does the equation $\tan(x)=y$ have any non-zero rational solution?

Published on 17 Nov 2014 - 3:37

291

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Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$

Published on 18 Nov 2014 - 23:53

66

Views

Functional derivative of a repeated integral

Published on 29 Mar 2026 - 2:30

192

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Nonlinear Functional Equation $f(x)^{2}=f\left(\frac x a\right)$

Published on 19 Nov 2014 - 20:48

2.9k

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Functions that satisfy $f(x+y)=f(x)f(y)$ and $f(1)=e$

Published on 21 Nov 2014 - 16:04

187

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Find all functions $f:\mathbb R\to\mathbb R$ such that $f\big(yf(x)\big)=x^2y^4$

Published on 22 Nov 2014 - 9:16

1.3k

Views

Solve the functional equation $2f(x)=f(ax)$ for some $a$.

Published on 22 Nov 2014 - 17:25

List Question

Solving an integral (or series) equations system

Functional equation $f(x)-f(y)=\frac{1}{(x-y)^{2}}$

functional equation for $x^2$ $f(f(x))=x^4$

Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$

A functional equation with no solution

About an integral equation

Find all odd functions $f: \mathbb{R} \to \mathbb{R}$ satisfying $f(t+1)=f(t)+1$ and $f\left(\frac{1}{t}\right)=\frac{1}{t^2}f(t)$

Find all polynomials with real coefficients that satisfy $(x^2-6x+8)P(x)=(x^2+2x)P(x-2)$

Does the equation $\tan(x)=y$ have any non-zero rational solution?

Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$

Functional derivative of a repeated integral

Nonlinear Functional Equation $f(x)^{2}=f\left(\frac x a\right)$

Functions that satisfy $f(x+y)=f(x)f(y)$ and $f(1)=e$

Find all functions $f:\mathbb R\to\mathbb R$ such that $f\big(yf(x)\big)=x^2y^4$

Solve the functional equation $2f(x)=f(ax)$ for some $a$.

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