The Functional Equation $ ( x + y ) \big( f ( x ) - f ( y ) \big) = ( x - y ) f ( x + y ) $, need solution have answer
129599
Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$
142873
What does the function f: x ↦ y mean?
13086
Overview of basic facts about Cauchy functional equation
77071
Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$
134880
Is there a difference between $y(x)$ and $f(x)$
32432
Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
121455
$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
67594
Books on functional equations
62111
Functional Equation $f(mn)=f(m)f(n)$.
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Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$
32599
Solution to the functional equation $f(x^y)=f(x)^{f(y)}$
43667
Is $f(x,y(x))$ a function of two variables? If so, how is that possible?
17175
Problem in solving functional equation $f(x^2 + yf(x)) = xf(x+y)$
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$