$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$
81799
Examples of functions where $f(ab)=f(a)+f(b)$
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
155806
(Olympiad Question) $f(2x) + 2f(y) = f(f(x+y))$
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
129902
If $f(x)=x+\int_{0}^{1}[xy^2+x^2y]f(y)dy$ where $x$ and$y$ are independent variable.Find $f(x).$
103934
Functional Equation (no. of solutions): $f(x+y) + f(x-y) = 2f(x) + 2f(y)$
35556
$f(z)=\frac{z}{1+|z|} $ Is 1-1?
77133
$g'(x) = \frac{1}{x}$ for all $x > 0$ and $g(1) = 0$. Prove that $g(xy) = g(x) + g(y)$ for all $x, y > 0$.
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
13248
How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
26219
Suppose f is a function such that f'(x) = 1/x for all x > 0. Prove that if f(1) = 0, then f(xy) = f(x) + f(y) for all x,y > 0
6482
Why aren't the functions $f(x) = \frac{x-1}{x-1}$ and $f(x) = 1$ the same?
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
28088
When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$
72906
Is $\frac{\partial}{\partial x_1}=\frac{\partial}{\partial y_1}$ if $x_1=y_1$?