New posts in functional-equations

Is Zorn's lemma necessary to show discontinuous $f\colon {\mathbb R} \to {\mathbb R}$ satisfying $f(x+y) = f(x) + f(y)$?

real-analysis set-theory functional-equations axiom-of-choice

Showing that $f(x)=\frac x{x+1}$ is the unique function satisfying $f(x)+f\left(\frac1x\right)=1$ and $f(2x)=2f\big(f(x)\big)$

algebra-precalculus contest-math functional-equations

Solution of a function equation $f(x) + f(y) = f(x + y + 2f(xy))$

functional-equations

Solve for $f(x)$ if $f(f(x))=6x-f(x)$

algebra-precalculus functions functional-equations

If $f(x)-f^{-1}(x)=e^{x}-1$, what is $f(x)$?

functional-equations inverse-function

Solve the functional equation $f(x)f(1/x)=f(x+1/x)+1$, $f(1)=2$, where $f(x)$ is a polynomial.

polynomials functional-equations

$f(ax)=f(x)^2-1$, what is $f$?

complex-analysis dynamical-systems functional-equations entire-functions

Do there exist functions $f$ such that $f(f(x))=x^2-x+1$ for every $x$?

algebra-precalculus functional-equations

Function that is both midpoint convex and concave

real-analysis functions functional-equations

Classifying Functions of the form $f(x+y)=f(x)f(y)$ [duplicate]

real-analysis functional-equations

Does $f(x+1)-f(x)$ constant imply $f$ is linear?

functional-equations

Functional equation: what function is its inverse's reciprocal? [duplicate]

inverse functional-equations inverse-function

Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function?

calculus functions functional-equations

IMO 1987 - function such that $f(f(n))=n+1987$ [closed]

elementary-number-theory functions induction contest-math functional-equations

Let $f: \mathbb N \rightarrow \mathbb N$ are increasing function such that $f\left(f(n)\right)=3n$. Find $f(2017)$ [duplicate]

functions functional-equations

Solution to the functional equation $f(x^y)=f(x)^{f(y)}$

exponential-function exponentiation functional-equations

Proving $f'(1)$ exist for $f$ satisfying $f(xy)=xf(y)+yf(x)$

calculus real-analysis derivatives functional-equations

Find all functions that satisfy $f(x^2f(y)^2)=f(x)^2f(y)$.

contest-math functional-equations

If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$

analysis functional-equations

If $ f(x \cdot f(y) + f(x)) = y \cdot f(x) + x $, then $f(x)=x$

functional-equations rational-numbers