Newbetuts

Find all functions $f: \mathbb{R} \rightarrow \mathbb {R}$ such that $f(x+y)+f(x-y)=2f(x)\cos y$ [duplicate]

Two variable functional equation: $f(x+y)+f(x-y)=2f(x)\cos y$ [duplicate]

Trying to solve $\frac{f(x) f(y) - f(xy)}{3} = x + y + 2$ for $f(x)$

Solving for the implicit function $f\left(f(x)y+\frac{x}{y}\right)=xyf\left(x^2+y^2\right)$ and $f(1)=1$

A functional equation in a TST exam

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

Condition for an additive function to be continuous

Finding all differentiable $f: [0,+\infty) \rightarrow [0,+\infty)$ such that $f(x) = f'(x^2)$ and $f(0)=0$

$f,g$ such that $\int fg = \int f \int g$

$f(x+y)f(x-y)=[f(x)f(y)]^2$ implies $f(x)=g\left(x^2\right)$ for some $g$

Functional Equation simple problem

The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $

How find all $f:\mathbb R\to\mathbb R$ such that $f\bigl(x\cdot f(y)\bigr)=y\cdot f(x)+kxy$

About the derivative of a function defined on rational numbers

Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$

Find all $f: \mathbb{R} \to \mathbb{R}$ such that $(f(x)+y)(f(x-y)+1)=f(f(xf(x+1))-yf(y-1)), \forall x,y \in \mathbb{R}$

The Notorious Triangle Problem

Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$

New posts in functional-equations

How to solve this functional equation $f(xf(y))+y+f(x)=f(x+f(y))+yf(x)$?

Which functions share a certain property of sinusoids?

Find all functions $f: \mathbb{R} \rightarrow \mathbb {R}$ such that $f(x+y)+f(x-y)=2f(x)\cos y$ [duplicate]

Two variable functional equation: $f(x+y)+f(x-y)=2f(x)\cos y$ [duplicate]

Trying to solve $\frac{f(x) f(y) - f(xy)}{3} = x + y + 2$ for $f(x)$

Solving for the implicit function $f\left(f(x)y+\frac{x}{y}\right)=xyf\left(x^2+y^2\right)$ and $f(1)=1$

A functional equation in a TST exam

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

Condition for an additive function to be continuous

Finding all differentiable $f: [0,+\infty) \rightarrow [0,+\infty)$ such that $f(x) = f'(x^2)$ and $f(0)=0$

$f,g$ such that $\int fg = \int f \int g$

$f(x+y)f(x-y)=[f(x)f(y)]^2$ implies $f(x)=g\left(x^2\right)$ for some $g$

Functional Equation simple problem

The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $

How find all $f:\mathbb R\to\mathbb R$ such that $f\bigl(x\cdot f(y)\bigr)=y\cdot f(x)+kxy$

About the derivative of a function defined on rational numbers

Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$

Find all $f: \mathbb{R} \to \mathbb{R}$ such that $(f(x)+y)(f(x-y)+1)=f(f(xf(x+1))-yf(y-1)), \forall x,y \in \mathbb{R}$

The Notorious Triangle Problem

Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$