List questions from functional-equations | MathQA

Finding all $ f : \mathbb R \to \mathbb R $ satisfying $ f \bigl ( f ( x ) f ( y ) \bigr ) + f ( x + y ) = f ( x y ) $ for all $ x , y \in \mathbb R $

Published on 18 Jul 2017 - 18:07

Functional equation: $ f \left( x + y ^ 2 + z ^ 3 \right) = f ( x ) + f ^ 2 ( y ) + f ^ 3 ( z ) $

Published on 19 Jul 2017 - 4:22

Function on real plane with strange condition

Published on 28 Mar 2026 - 9:44

A functional equation $\varphi(x) = \epsilon(x)\epsilon(x+x_1)\varphi(x+x_2)$

Published on 21 Jul 2017 - 16:31

Summation of a strictly increasing and completely multiplicative function satisfying $f(2)=2$

Published on 21 Jul 2017 - 16:55

Find all functions satisfying $f\left(f(x)f(y)\right)+f(x+y)=f(xy)$

Published on 22 Jul 2017 - 2:49

A continuous functions such that $f(x)=f(2x+1)$ is constant

Published on 23 Jul 2017 - 12:03

Fuctional equation with derivatives

Published on 24 Jul 2017 - 4:43

How do we know this is the unique solution to this functional equation?

Published on 24 Jul 2017 - 6:16

The functional equation $f\bigl(x+yf(x)\bigr)+f\bigl(xf(y)-y\bigr) = f(x)-f(y)+2xy^2$

Published on 24 Jul 2017 - 9:11

Finding all functions $f : \mathbb{R} \rightarrow \mathbb{R}$ with the given property

Published on 25 Jul 2017 - 5:33

Functional equations in the form $f(x)-f(x-c)=P_n(x)$

Published on 25 Jul 2017 - 12:18

$ U(x+y) = U(x) V(y) W(y) + U(y) V(x) W(y) + U(y) V(y) W(x) + U(y) V(x) W(x) + U(x) V(y) W(x) + U(x) V(x) W(y) $

Published on 28 Jul 2017 - 12:49

how to solve this equation for $ f(x) $ in a functional equation

Published on 25 Mar 2026 - 20:15

Finding period of function from the functional relation $f(x+T) = 1 + \left(2f(x)-f(x)^2\right)^{\frac12}$

Published on 02 Apr 2026 - 21:17