A discontinuous function such that $f(x + y) = f(x) + f(y)$
13086
Overview of basic facts about Cauchy functional equation
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
121455
$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
18511
Can we construct a function that has uncountable many jump discontinuities?
19474
Find all solutions to the functional equation $f(x) +f(x+y)=y+2 $
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
73519
Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
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 $
66951
Proving the existence of a sequence of functions converging to 0 with an added property
7358
For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous.
52486
Is there a function that is contiunous at all the rationals, and discontinuous at all the irrationals?
62817
Functions which are Continuous, but not Bicontinuous
15820
Discontinuous linear functional
38886
Discontinuous function on Q
74950
Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$