If $f:[0,\infty)\to [0,\infty)$ and $f(x+y)=f(x)+f(y)$ then prove that $f(x)=ax$
13086
Overview of basic facts about Cauchy functional equation
49882
Proving $f(x,y,z)=\big(\frac{x}{a+x+y+z}, \frac{y}{a+x+y+z}, \frac{z}{a+x+y+z} \big)$ is injective
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 $f(t)=c\cdot e^t$.
26219
Suppose f is a function such that f'(x) = 1/x for all x > 0. Prove that if f(1) = 0, then f(xy) = f(x) + f(y) for all x,y > 0
59063
$f(f(x))=f(x)$ question
112285
Show that $\lim_{x\to\infty} f(x)=0 \implies \lim_{x\to\infty} f'(x)=0$
46844
Show that if $\int_0^x f(y)dy \sim Ax^\alpha$ then $f(x)\sim \alpha Ax^{\alpha -1}$
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
89537
$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
145573
How to show that $f$ is a zero function?
60348
How do I prove $F(a)=F(a^2)?$
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
38831
If $\lim_{x\to+\infty}[f(x+1)-f(x)]= \ell,$ then $\lim\limits_{x\to+\infty}\frac{f(x)}x=\ell$.
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
24553
$f$ has the form $f(x) =ax^2+bx+c$.
121771
Proof $f(x)\equiv 0$