# Questions tagged [functions]

For elementary questions about functions, notation, properties, and operations such as function composition. Consider also using the (graphing-functions) tag.

34,033 questions
Filter by
Sorted by
Tagged with
22 views

### Fully spanning subset

Consider a finite multiset of integers denoted by M. I define a subset of that multiset denoted by A. I say that A is a Fully Spanning Sub-set of M if, for every item x in M, if ...
30 views

### A surjective continuous open map has a continuous right inverse [duplicate]

My question arises from this post and similar questions. It's clear that for an open, onto and continuous function $f:X\rightarrow Y$, not every right inverse is continuous, but my question is if ...
• 800
111 views

### Solutions to $(f(x)-f(y))^3=f\left(x^3\right)-f\left(y^3\right)$

I was wondering, if there are more solutions to the functional equations, than $f(x) = const$. Maybe someone has an idea of how to find all solutions (or all continuous solutions)? Find all the ...
1 vote
55 views

### Finding a function in the unit sphere of a functional subspace with a couple of properties

Preliminaries: A={f $\in C(X); f(a)=0$} is a banach space with norm the following: $\Vert f\Vert=sup\vert f(x)-f(y)\vert; x,y \in X$ ( X is Hausdorff and compact space. Element of a is in X. ...
45 views

### Limit of a function when 'a' is not in the domain [closed]

Is this a correct statement that as x approaches to 'a' for f(x) where 'a' does not belong to the domain of f(x) then the limit at 'a' does not exist
54 views

### Closed form for the area under $f(x):=\lim_{N \to \infty}\frac{\pi(Nx)}{\pi(N)}$

Define a function $f:\Bbb Q \to \Bbb Q$ by the following $$f(x):=\lim_{N \to \infty}\frac{\pi(Nx)}{\pi(N)}$$ where $\pi(\cdot)$ is the prime counting function and $N\in \Bbb N.$ I would like to find ...
• 756
2k views

• 166
29 views

### Derivation of Legendre Polynomials from only orthogonality

I recently stumbled on the idea of Legendre polynomials, from the perspective of using them to approximate functions over a region, and I discovered all of these other ways to express them, using ...
• 380
### Determining $t(x)$ from $\frac{dx}{dt}$?
I have a question that "feels" basic/stupid, but I've been really struggling with it. The basic question is: is there an easy way to determine $t(x)$ from $x(t)$ or $\frac{dx}{dt}$? To ...