New posts in functional-equations

Find all functions on the non-zero reals to itself satisfying $f(xy)=f(x+y)(f(x)+f(y))$

algebra-precalculus functions functional-equations

Which positive continuous functions satisfy $F(x) = F(e^x)-F(e^{-x})$ for $x\geq 0$?

sequences-and-series stochastic-processes taylor-expansion functional-equations

find functions f such that $f(f(x))=xf(x)+1$,

functional-equations

Function preserving exponentiation [duplicate]

functional-equations

let $f(\frac{x}{3})+f(\frac{2}{x})=\frac{4}{x^2}+\frac{x^2}{9}-2$ then find $f(x)$

algebra-precalculus functional-equations

A functional relation which is satisfied by $\cos x$ and $\sin x$

calculus analysis recreational-mathematics contest-math functional-equations

Proving that this function has the same value for all integers $\geq4$. [duplicate]

algebra-precalculus number-theory elementary-number-theory functions functional-equations

Is there a function $f(x)$ that satisfies $f(e^x) = e^x f(x)$?

partial-differential-equations continuity functional-equations

Solving the functional equation $f(x+1) - f(x-1) = g(x)$

functions functional-equations

How find this all function $f(x^n+2f(y))=(f(x))^n+y+f(y)$

functional-equations

if $f(x + y) = f(x)f(y)$ is continuous, then it has to be injective.

functions continuity exponential-function functional-equations

Maps of $\mathbb{R}^3$ commuting with the cross product

geometry analytic-geometry functional-equations cross-product

How do you solve $f'(x) = f(f(x))$?

ordinary-differential-equations functional-equations

How find this function equation $(f(x))^2-(f(y))^2=f(x+y)\cdot f(x-y)$

contest-math functional-equations

Solving the functional equation $f(xy)=f(f(x)+f(y))$

algebra-precalculus functional-equations

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

polynomials functional-equations

Find all real to real function satisfy this functional equation.! $f((x+y)/(x-y))=[f(x)+f(y)]/[f(x)-f(y)]$

functional-equations

What are some examples of Idempotent functions?

algebra-precalculus functions functional-equations

Converse of Taylor's Theorem

real-analysis numerical-methods taylor-expansion functional-equations approximation-theory

Solving $f(x+f(y)) = f(x) + y$

functional-equations