$f(a+b)=f(a)+f(b)$. Prove that $f(x)=Cx$, where $C=f(1)$
13086
Overview of basic facts about Cauchy functional equation
125788
A function with a property $f(x+y)=f(x)f(y)$
24553
$f$ has the form $f(x) =ax^2+bx+c$.
107173
If $a\lt{b}$ and $c\le{d}$, prove that $a+c\lt b+d$
155806
(Olympiad Question) $f(2x) + 2f(y) = f(f(x+y))$
31732
If the function $f$ satisfies the equation $f(xf(y)+x)=xy+f(x)$, find $f$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
47135
Prove if a = b, then f(a) = f(b) for any function f (with natural deduction)
15262
Prove $\exists \xi, \eta \in (0,1)$, such that $f(\xi)+f'(\eta)=\xi+\eta$.
85612
Let functions $ f: A \to B$ and $g: B \to A$, suppose that $ g \circ f = i_A$. Prove that if $f$ is onto, then $g$ is one-to-one
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
132093
Solve $f(f(x))=f(x)$
19355
prove $f(x)=x^3+x$ is one to one and onto
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$