New posts in functional-equations

If $f(f(x)) = x+1, f(x+1) = f(x) + 1$, is it true that $f(x) = x + 1/2$?

calculus functional-equations iterated-function-system

Prove that there is no function $f:\Bbb{R}\to\Bbb{R}$ with $f(0)>0$ such that $\forall x,y\in\Bbb{R}, f(x+y)\geq f(x)+y f(f(x))$

calculus real-analysis limits functional-equations

Functional equation of irreducible characters

representation-theory functional-equations finite-groups characters

Solve functional equation $(x+y)(f(x)-f(y))=f(x^2)-f(y^2)$ [duplicate]

functional-equations

Find a solution for $f\left(\frac{1}{x}\right)+f(x+1)=x$

calculus real-analysis functional-equations

Are there continuous functions $f,g:\mathbb{R}\longrightarrow\mathbb{R}$ such that for any $x$, $f(g(x))=\sin x$ and $g(f(x))=\cos x$?

real-analysis functions functional-equations

What is the derivative of $f(x)$ if $f(x)+f(y)=f\left(\frac{x+y}{1-xy}\right)$?

derivatives functional-equations

Finding $f$ such that $f(f(f(f...(x)))) = x$

real-analysis functional-equations

Help remembering a Putnam Problem [duplicate]

functional-equations contest-math

The value of the trilogarithm at $\frac{1}{2}$

special-functions functional-equations

Prove that $f(x)=8$ for all natural numbers $x\ge{8}$

functional-equations

If $f(x)^2=x+(x+1)f(x+2)$, what is $f(1)$?

functions functional-equations nested-radicals

Find all $f(x)$ such that $x(f(x+1)-f(x))=f(x)$

algebra-precalculus functional-equations

A function satisfying $f(\frac1{x+1})\cdot x=f(x)-1$ and $f(1)=1$?

calculus functions functional-equations

Are $f$ satisfying $|f(y)| = |f(x+y) - f(x)|$ additive?

linear-algebra functional-equations

If $\frac{f(x^2)}{f(x)}=1+x+x^2+\ldots+x^7$ then what is $f(x)$?

functions functional-equations calculus

How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$

contest-math functional-equations

Finding $f$ from the functional equation $f(x+y)=f(x) + f(y) + e^{x+y}(x+y)-xe^x-ye^y+2xy$

functions functional-equations

Find all functions of positive integers for $f(f(n))=n+2$

induction functional-equations integers

a continuous function satisfying $f(f(f(x)))=-x$ other than $f(x)=-x$

functional-equations