Prove that there exists a unique function $f: [0, \infty) \to [0, \infty)$ which satisfies the equation $f(f(x))=6x-f(x)$
42699
Solve for $f(x)$ if $f(f(x))=6x-f(x)$
121771
Proof $f(x)\equiv 0$
17119
Find all strictly monotone $f:(0,+\infty) \to (0, +\infty)$ such that $f(\frac{x^2}{f(x)})=x.$
134043
Prove that for $ f(x+2\cdot\pi)=f(x), x \in \mathbb{R} $, there exists $ x_0 $ so $ f(x_0+\pi)=f(x_0) $
61640
Prove c exists for f:[0,1] -> R
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
76458
Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$
145573
How to show that $f$ is a zero function?
81
$\lim_{n\to \infty}f(nx)=0$ implies $\lim_{x\to \infty}f(x)=0$
113871
Prove $f(x) = \sqrt x$ is uniformly continuous on $[0,\infty)$
80210
It is posible to have a function $f$ with the following property?
155575
Proving a polynomial $f(x)$ composite for infinitely many $x$
99917
What function satisfies $F'(x) = F(2x)$?
36402
Prove that $f(x) = \cos(x)$ has a unique fixed point.
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
83338
Show that there's no continuous function that takes each of its values $f(x)$ exactly twice.