To find all functions $h:\mathbb{R}\to\mathbb{R}$ such that $h(x+y) = h(x)+h(y)$ and $h(xy)=h(x)h(y)$
32856
Functional equations $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$
39090
Finding functions such that $f(g(x)) = f(x)g(x)$
53168
Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
73519
Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
157744
Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
34077
Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
129599
Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$
12825
Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$
141938
Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$
40868
Composition of two functions - Bijection
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 $
104949
How would I prove that this function is affine if $f(x+h)-f(x)=hf'(x)$?
27188
Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$