Function that satisfies $f(x+ y) = f(x) + f(y)$ but not $f(cx)=cf(x)$
13086
Overview of basic facts about Cauchy functional equation
134880
Is there a difference between $y(x)$ and $f(x)$
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 $f'(x) = f(1+x)$
139019
Polynomial satisfying $f(x) = f'(x) \cdot f''(x)$
28088
When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$
146719
Functional equation $f(r \cos \varphi)+f(r \sin \varphi)=f(r)$
32856
Functional equations $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
81799
Examples of functions where $f(ab)=f(a)+f(b)$
48925
BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$
111556
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?
151819
A twice differentiable function $f$ satisfies $f′′(x)+f(x)=−xg(x)f′(x)$, $\forall x\ge 0$.
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
97772
An example of a function which satisfies $\sup_{y}\inf_{x}f(x,y)<\inf_{x}\sup_{y}f(x,y)$
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
136475
d'Alembert-like functional equation: $f(x+y)+g(x-y)=\lambda f(x)g(y)$