Functions $f:\mathbb R \to \mathbb R$ which satisfy $f(x^2+f(y))=y+(f(x))^2$
35281
$1992$ IMO Functional Equation problem
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
149328
A function such that $f:\mathbb C \to \mathbb C$ such that $f(z)f(iz)=z^2$ satisfies $f(z)+f(-z)=0$.(MADHAVA-2020)
34260
Injective function from $\mathbb{R}^2$ to $\mathbb{R}$?
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 $f(x)^2=f(x^2)$
24553
$f$ has the form $f(x) =ax^2+bx+c$.
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
29403
Finding functions $f: \Bbb R_*^+ \to \Bbb R_*^+$ with certain properties
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
74950
Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$
144473
Finding all functions $ f : \mathbb N^*\to\mathbb N^*$ such that for every $ x , y \in \mathbb N ^ * $, $ f ( x ) + f ( y ) \mid x ^ n + y ^ n $
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$