Help with the functional equation $f(x - f(y)) = f(f(y)) + 2 x f(y) + f(x) - 1$
55693
The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
131586
Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
147195
Help needed in finding the value of $f(2001)$ in the given functional equation
53024
$f(x)f(1/x)=f(x)+f(1/x)$
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
139436
Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem
81055
Functional Equation simple problem
110704
Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
65418
Solve these functional equations: $\int_0^1\!{f(x)^2\, \mathrm{dx}}= \int_0^1\!{f(x)^3\, \mathrm{dx}}= \int_0^1\!{f(x)^4\, \mathrm{dx}}$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
76458
Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.