The function $f : \mathbb{R} \to \mathbb{R}$ satisfies $f(x) f(y) = f(x + y) + xy$for all real numbers $x$ and $y.$ Find all possible functions $f.$
48925
BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$
76458
Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$
99917
What function satisfies $F'(x) = F(2x)$?
153942
Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$
133333
Find $f(x)$ for $f(f(x))=\sin x$
30855
Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
103934
Functional Equation (no. of solutions): $f(x+y) + f(x-y) = 2f(x) + 2f(y)$
59063
$f(f(x))=f(x)$ question
111556
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
77071
Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
132093
Solve $f(f(x))=f(x)$
121455
$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$