Help working with the functional equation $f(a) f(b) = f(a+b) + ab$
48925
BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$
55286
Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$
66867
Question regarding the function $z=a+bi \mapsto f(z)=a+i(a+b)$.
146719
Functional equation $f(r \cos \varphi)+f(r \sin \varphi)=f(r)$
25953
Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
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 $
80421
Show that $a - b \mid f(a) - f(b)$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
67594
Books on functional equations
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
39090
Finding functions such that $f(g(x)) = f(x)g(x)$
116270
Functional equations leading to sine and cosine
157744
Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
88683
Functional equation $f\left(\frac{x+y}{2}\right)+f\left(\frac{2xy}{x+y}\right)=f(x)+f(y)$ implies $2f(\sqrt{xy})=f(x)+f(y)$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
111556
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?