If $f(rx)=r^{\alpha} f(x)$, then which of these options is true?
96539
is $f$ constant or dilation
47026
if $f^{(n)}(x_0),g^{(n)}(x_0)$ exist and $\lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n}=0$ then $f^{(r)}(x_0)=g^{(r)}(x_0 )$ for all $0\leq r\leq n.$
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
78307
Under what conditions is $AA^T$ invertible?
39082
Proving $x^\alpha-\alpha x \le 1- \alpha $
152105
When is $x^{\alpha}\sin(x^{\beta})$ uniformly continuous for $\alpha, \beta > 0$?
62744
Does the functional equation $f(1/r) = rf(r)$ have any nontrivial solutions besides $f(r) = 1/\sqrt{r}$?
99827
For what values will f(x) be necessarily one-one?
82448
Why is $f(x) = x\phi(x)$ one-to-one?
29628
How to find a nonlinear function $f:\mathbb{R}^2\to\mathbb{R}^2$ that is almost linear in the sense $f(\alpha (a,b))=\alpha f(a,b)$?
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
98271
Why does $(x \to a) ≠ (x = a)$ , But $f(x \to a) = f(x = a)$
32063
if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
12217
What is so special about $\alpha=-1$ in the integral of $x^\alpha$?