Functional Equation in the rationals: $f(xy)=f(x)f(y)-f(x+y)+1$
77071
Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$
151519
If $f(f(x))=x^2-x+1$, what is $f(0)$?
73519
Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
13042
Finding a function from the given functional equation .
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
147195
Help needed in finding the value of $f(2001)$ in the given functional equation
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
19019
Find all functions $f:\Bbb{Q}\rightarrow \Bbb{Q}$ such that $f(x)+f(t)=f(y)+f(z)$ for all rational numbers $x<y<z<t$ that form an AP
48925
BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
35066
Nature and number of solutions to $xy=x+y$
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
11806
Functional equation.
6680
Solve for all possible functions f: $|f(x)-f(y)|=2|x-y|$.
139436
Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem
128751
Solving for $f(2004)$ in a given functional equation
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$