Existence of a Noncontinous $f$ Satisfying $f(a+b) = f(a)+f(b)$
13086
Overview of basic facts about Cauchy functional equation
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
97772
An example of a function which satisfies $\sup_{y}\inf_{x}f(x,y)<\inf_{x}\sup_{y}f(x,y)$
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
53627
Proving continuity of $f$
77943
If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
15262
Prove $\exists \xi, \eta \in (0,1)$, such that $f(\xi)+f'(\eta)=\xi+\eta$.
134043
Prove that for $ f(x+2\cdot\pi)=f(x), x \in \mathbb{R} $, there exists $ x_0 $ so $ f(x_0+\pi)=f(x_0) $
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
13927
Values of $a$ s.t. for all continuous $f$ with $f(0)=f(1)$ there exists $x$ s.t. $f(x+a) = f(x)$
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
80199
Do we have always $f(A \cap B) = f(A) \cap f(B)$?
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.