How do I find a function $f$ such that $f(x^2)=2f(x)$?
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
31732
If the function $f$ satisfies the equation $f(xf(y)+x)=xy+f(x)$, find $f$
25953
Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
113045
How do I find the inverse of $f(x) = \frac{x}{x^2 + 1}$
50552
find functions that $f(m+k)=f(mk-n)$
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
55175
Is the function $f(x) = x^2 - 2x$ one-to-one?
66406
How to calculate $f(x)$ in $f(f(x)) = e^x$?
124523
Finding an Inverse Function and Composition of Functions?
34343
Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
42699
Solve for $f(x)$ if $f(f(x))=6x-f(x)$
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
6680
Solve for all possible functions f: $|f(x)-f(y)|=2|x-y|$.
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$