# Tagged Questions

21 views

### Help with function $f_r(x^q)=q^rx^{q-1}$

Let $r,q$ be a positive integers. I am looking for a function $f_r(x^q)$ such that it is satisfied $$f_r (x^q)=q^r x^{q-1}$$ (without explicit dependence on $q$ of course, and for $r>1$). I ...
24 views

### Keep a Function Positive via Mod

I have a function $F$ and I want it to remain positive--i.e., $$- F=F,\quad F=F$$ Would sticking a $\mod 2$ in front of $F$ do this? That is, because $$-1\mod 2=1\mod 2=1$$ Then let ...
33 views

### Is there a name for this property of a real function?

Let $M=\sup_{x \in [0,1]^n} f(x)$ where $f:[0,1]^n \rightarrow \mathbb{R}$ is differentiable twice, and write $x=(x_1, \dots, x_n)$. Let $M_{x_i=0}=\sup_{x \in [0,1]^n:x_i=0} f(x)$ and ...
705 views

### What are the most important functions every mathematician should know? [closed]

I am an undergrad in math and was wondering, what are for you the most important functions every mathematician should know? At the moment I think ...
35 views

### composite function problem

If I have the following expression: $$g(f(x))-g(x)=1,$$ it is possible to express $f(x)$ in terms of the $g(x)$: $$f(x)=g^{-1}(1+g(x)).$$ Is it possible to express $g(x)$ in terms of $f(x)$?
38 views

### In the space $L^2 [0,1]$ to solve for all values ​​of the complex parameters $\lambda$ and $b:$ [closed]

In the space $L^2 [0,1]$ to find a solution of the integral equation for all values ​​of the complex parameters $\lambda$ and $b$: $x (t)-λ\int_0^1 t^2s^2x(s) \, ds = 4t + bt^2$