If two functions f,g are both discontinuous at some point a in the domain, does this mean that the sum f+g is also discontinuous at a?
88240
Two functions discontinuous, but sum continuous
144323
Differentiation of a function
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
112566
Let $f,g$ be two distinct functions from $[0,1]$ to $(0, +\infty)$ such that $\int_{0}^{1} g = \int_{0}^{1} f $.
150833
Discontinuities of the derivative of a differentiable function on closed interval
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.
146480
Example of $\deg(fg)<\deg(f)+\deg(g)$
43956
Differentiating $f(x)^{g(x)}$
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
15820
Discontinuous linear functional
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 $\mathbb R$
100283
How to understand the notion of a differential of a function
130023
Prove that the sum of two continuous functions is continuous
87131
Discontinuous at rationals and differentiable at irrationals?
80210
It is posible to have a function $f$ with the following property?
6417
Can a function be differentiable at the end points of its (closed interval) domain?
2321
Can there be two distinct, continuous functions that are equal at all rationals?