Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that $f(x^2 + y + f(y)) = 2y + (f(x))^2$
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
13248
How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
14975
Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
141938
Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
129902
If $f(x)=x+\int_{0}^{1}[xy^2+x^2y]f(y)dy$ where $x$ and$y$ are independent variable.Find $f(x).$
62966
Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
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 $x,y\in\mathbb{R}$.
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
67848
Let $A$ be the set of all functions $f:\mathbb{R}\to\mathbb{R}$ that satisfy the following two properties.
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
24862
Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$