Find all functions $f$ such that $f\left(x^2-y^2\right)=(x-y)\big(f(x)+f(y)\big)$.
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
34343
Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
129052
Find all functions satisfying $\frac{1}{f(a)}+ \frac{1}{f(b)} = \frac{1}{f(c)} $ whenever $\frac{1}{a}+ \frac{1}{b} = \frac{1}{c} $
157756
Examine if function $f:\mathbb{R^2}\rightarrow \mathbb{R^2}$ which is defined as $f(x,y)=(2x-y,x-4y)$ is bijective. If bijective, find $f^{-1}$.
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
50833
Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.
144445
Functions $f:\mathbb{N}\rightarrow \mathbb{Z}$ such that $\left(m-n\right) \mid \left(f(m)-f(n)\right)$
55286
Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$
131586
Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $
89257
Give an example of a function $f:\mathbb{R}^2 \mapsto \mathbb{R}^2$ such that
19019
Find all functions $f:\Bbb{Q}\rightarrow \Bbb{Q}$ such that $f(x)+f(t)=f(y)+f(z)$ for all rational numbers $x<y<z<t$ that form an AP
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
139436
Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem
25953
Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
141852
Prove that $2\int_a^b \int_a^x f(x)f(y) \, dy \, dx = \left[ \int_a^b f(x) \, dx \right]^2$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$