Find all functions $f\colon \mathbb R \to \mathbb R$ such that $f(f(x)(y + 1)) = x[f(y) + 1]$, $\forall x, y \in \mathbb R$.
55286
Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
62723
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
19474
Find all solutions to the functional equation $f(x) +f(x+y)=y+2 $
86473
Find all entire functions such that $|f(z)|\leq |\sin(z)|$ for all $z\in\mathbb C$.
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
65946
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
64339
Find $f$ where $f'(x) = f(1+x)$
1071
Determine all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $xf(y)+yf(x)=(x+y)f(x^2+y^2)$ for all $x,y\in\mathbb{N}$ (contest question)
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
75448
Find all function satisfying $f(f(n))+f(n)=2n+3k$
67848
Let $A$ be the set of all functions $f:\mathbb{R}\to\mathbb{R}$ that satisfy the following two properties.
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
125788
A function with a property $f(x+y)=f(x)f(y)$