New posts in functional-equations

Solving the infinite radical $\sqrt{6+\sqrt{6+2\sqrt{6+3\sqrt{6+...}}}}$

functional-equations nested-radicals

How to go about finding a function that satisfies $f(x)=-f(x-1)^{2}+2^{2^{x-3}}f(x-1)+2^{2^{x-2}}$ (Or determining if such a function exists)

functional-equations

Let $f:\mathbb{R} \to \mathbb{R}$ continuous with $f(f(x))=e^x$, show that $\lim_{x\to \infty } \frac{f(x)}{x^n}=\infty$ (Brazilian Olympiad)

real-analysis limits contest-math functional-equations

Proof of Cauchy's functional equation

real-analysis proof-explanation functional-equations

Continuous and additive implies linear

real-analysis linear-algebra analysis functional-equations

$g(x+y)+g(x)g(y)=g(xy)+g(x)+g(y)$ for all $x,y$.

contest-math functional-equations

Strange functional equation: $f(x)+f(\cos(x))=x$

real-analysis functional-equations

A function whose antiderivative equals its inverse.

functional-equations

$f:\mathbb{R} \to \mathbb{R}$ such that $f(x+y^2+f(y)) = f(x-y^2-f(y))$

functions functional-equations substitution

Proving that $f(n)=n$ if $f(n+1)>f(f(n))$

functional-equations

$f(x+1)=f(x)+1$ and $f(x^2)=f(x)^2$

functional-equations

Find closed form of $f(x)= \frac{1}{x} \sum_{i=1}^{k} f(x+i)$

functional-equations gamma-function

Is my proof that $f(x)$ where $f(f(x)) = 6x - f(x)$ for all $f:R+→R+$ is linear correct?

functions contest-math functional-equations

Is there any non-constant function $f(x)$ satisfying $f(x) f(y) = f(x) + f(y)$?

functional-equations

$f(f(x))=f(x)$ question

analysis functional-equations function-and-relation-composition

Given $f(f(x))$ can we find $f(x)$?

algebra-precalculus functions functional-equations

Find polynomials such that $(x-16)p(2x)=16(x-1)p(x)$

real-analysis analysis functional-equations

How to find all polynomials satisfying $P(x^2+x-4)=P^2(x)+P(x)$?

polynomials functional-equations

If $f$ is continuous and $f(x+y)=f(x)f(y)$, then $\lim\limits_{x \rightarrow 0} \frac{f(x)-f(0)}{x}$ exists

calculus limits functional-equations

Is a function that preserves the cross product necessarily linear in $\mathbb R^3$? $f(a) \times f(b) = a \times b$ [closed]

linear-algebra functional-equations cross-product