Proving the uniqueness of a solution to $f(x-f(y)) = f(f(y)) + xf(y) + f(x) - 1$
34077
Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
44100
Prove that identity element is unique
55693
The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
103934
Functional Equation (no. of solutions): $f(x+y) + f(x-y) = 2f(x) + 2f(y)$
29096
Non-uniqueness of solutions of the heat equation
54729
Prove that $f$ has a fixed point .
17175
Problem in solving functional equation $f(x^2 + yf(x)) = xf(x+y)$
23465
When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?
89473
Uniqueness of minimal polynomial: $f(x)$ divides $g(x)$
14773
Finding distinct solutions for the equation
20568
Does the following have a solution for f(x,y)?
104949
How would I prove that this function is affine if $f(x+h)-f(x)=hf'(x)$?
76110
Proving that the zero vector is unique
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)