Newbetuts

Find all pairs of functions $(f,g)$, $\forall x, y \in \mathbb{R}, f(x+g(y))=x f(y) - y f(x) + g(x)$

How much does $(f \circ f)(x)=x^2 - x + 1$ determine $f$?

Vector Space Structures over ($\mathbb{R}$,+)

Find $f(f(\cdots f(x)))=p(x)$

Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$

Suppose a function $f : \mathbb{R}\rightarrow \mathbb{R}$ satisfies $f(f(f(x)))=x$ for all $x$ belonging to $\mathbb{R}$.

Which trigonometric identities involve trigonometric functions?

Functional Equation $f(x+y)-f(x-y)=2f'(x)f'(y)$

Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $

$f(x^2) = 2f(x)$ and $f(x)$ continuous

Determining if a differential equation has unique solution

Find $f(x)$ for $f(f(x))=\sin x$

Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$

If $f(3x)=f(x)$ and $f$ is continuous, show that $f(x)$ is a constant function.

New posts in functional-equations

How to prove that $f(f(x))=-x$ implies that $f$ is not continuous? [duplicate]

Solve the functional equation $2f(x)=f(ax)$ for some $a$.

Many other solutions of the Cauchy's Functional Equation

If the function $f$ satisfies the equation $f(xf(y)+x)=xy+f(x)$, find $f$

Show that $f(x) = x$ if $f(f(f(x))) = x$.

Find all functions $f:\mathbb R \to \mathbb R$ satisfying $xf(y)-yf(x)=f\left( \frac yx\right)$

Find all pairs of functions $(f,g)$, $\forall x, y \in \mathbb{R}, f(x+g(y))=x f(y) - y f(x) + g(x)$

How much does $(f \circ f)(x)=x^2 - x + 1$ determine $f$?

Vector Space Structures over ($\mathbb{R}$,+)

Find $f(f(\cdots f(x)))=p(x)$

Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$

Suppose a function $f : \mathbb{R}\rightarrow \mathbb{R}$ satisfies $f(f(f(x)))=x$ for all $x$ belonging to $\mathbb{R}$.

Which trigonometric identities involve trigonometric functions?

Functional Equation $f(x+y)-f(x-y)=2f'(x)f'(y)$

Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $

$f(x^2) = 2f(x)$ and $f(x)$ continuous

Determining if a differential equation has unique solution

Find $f(x)$ for $f(f(x))=\sin x$

Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$

If $f(3x)=f(x)$ and $f$ is continuous, show that $f(x)$ is a constant function.