What can be $f$ so that $f(f(x)) = -x$?
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
151519
If $f(f(x))=x^2-x+1$, what is $f(0)$?
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?
72769
How find this function $xf(x^2)=f(x),x>0$
30860
Prove that $f(x)=0$ in $[-1,1]$.
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
97773
If $f$ is continuous with $f(x) = f(2x),f(1) = 3$, then what is $ \int_{-1}^{1}f(f(x))\,dx$?
3387
Derivative of $f(x)=|x|$
147325
Proving that if $f(x)=x$ has no real solution then $f(f(x))=x$ has no real solution either
80210
It is posible to have a function $f$ with the following property?
129599
Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$
17310
Can $f(x)=|x|^3$ be differentiated
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
6482
Why aren't the functions $f(x) = \frac{x-1}{x-1}$ and $f(x) = 1$ the same?
42699
Solve for $f(x)$ if $f(f(x))=6x-f(x)$