Prove that $f(x)=x$.
104209
Functional equation - Cyclic Substitutions
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
105172
Prove that the entire function is constant over certain conditions.
15262
Prove $\exists \xi, \eta \in (0,1)$, such that $f(\xi)+f'(\eta)=\xi+\eta$.
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
82001
How to prove the function is a constant
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
89637
Proof that in a field $x=0$ is equivalent to $x=-x$
8854
Prove $f $ is identically zero if $f(0)=0$ and $|f'(x)|\le|f(x)|$
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
105700
Proving $\,f$ is constant.
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
71857
Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$