Functional equation $xf(x)=f(1/x)$
62744
Does the functional equation $f(1/r) = rf(r)$ have any nontrivial solutions besides $f(r) = 1/\sqrt{r}$?
13086
Overview of basic facts about Cauchy functional equation
148227
Rewriting of functional equation $f(xy)=f(x)+f(y)$
62111
Functional Equation $f(mn)=f(m)f(n)$.
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
59063
$f(f(x))=f(x)$ question
30860
Prove that $f(x)=0$ in $[-1,1]$.
71049
Functional equation $f(xy)=f(x)+f(y)$ and continuity
55286
Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$
24862
Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
157744
Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
88311
Linear functional f(v)=0 imply v=0
19474
Find all solutions to the functional equation $f(x) +f(x+y)=y+2 $
138481
$f(x)=x/1$ is not injective?
96495
Periodicity of a Function Given the Functional Equation $f(x+a)=\frac12+\sqrt{f(x)-\big(f(x)\big)^2}$
82448
Why is $f(x) = x\phi(x)$ one-to-one?