# Questions tagged [functions]

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

29,497 questions
Filter by
Sorted by
Tagged with
13 views

### How to find a function that gives me the indexes of a square matrix

Let a square matrix M with size m, and let i and j, given $0 \leq i = j < m$, so that $a_{ij}$ is a value of the matrix located in the row i and column j (assuming that we start counting with 0 ...
14 views

### How to customize a function with a horizontal asymptote?

I'm looking for a function that approaches a y-value as x approaches infinity, something close to: $$y=\frac{x}{x+1}$$ however I have no idea how to customize such a function to suit my needs. I know ...
26 views

89 views

54 views

### extension Rolle's theorem for limit values

Rolle's theorem states that: If a real-valued function $f$ is continuous on a proper closed interval $[a, b]$, differentiable on the open interval $(a, b)$, and $f (a) = f (b)$, then there exists at ...
62 views

16 views

...
42 views

### Solve a quartic function with three unknowns and two given roots.

I'd like to know how I could solve the following quartic function: $p(z)=2z^4+az^3+bz^2+cz+3$ given that it $2$ and $i$ should be part of their roots. I thought I should maybe be trying to turn this ...
41 views

### Formal Definition of the Product of Two Sets

I am taking a course in Algebraic Structures, and the notion of product of sets (a.k.a. Caratesian Product) came in. We were given a definition that made me feel I didn't understand it. They gave the ...
38 views

### $F(x, y) = \frac{x^2+y^2} {|x|+|y|}$ at $(x, y) \neq (0, 0)$ find if function is continuous or not? [closed]

$F(x, y) = \frac{x^2+y^2}{|x|+|y|}$ at $(x, y) \neq (0, 0)$ find if function is continuous or not? Continuity and Functions We have to tell whether function is continuous or not. I don't know how to ...
29 views

### What functions with source and target the rational numbers satisfy the intermediate value theorem?

I am curious to find if there is a characterization of the set $S$ of all functions $f: \mathbb{Q} \to \mathbb{Q}$ where for all intervals $[a,b] \subset \mathbb{Q}$, there exists $x \in [a,b]$ for ...
35 views

### I'm stuck with this proof: [closed]

Proof that -> $\lim\limits_{x\rightarrow 0^+}f(x) = \infty$ if, and only if $\lim\limits_{x\rightarrow \infty}f(\frac{1}{x}) = \infty$. Thanks everyone :D
74 views

### Using Lagrange multiplier , find minimum value of $xy(x^2 + y^2) +4$ , given that $x^2 + y^2 +xy -1 = 0 , x,y \in \mathbb R$
Using Lagrange multiplier , find minimum value of $$f(x,y)=xy(x^2 + y^2) +4$$ , Given that $g(x,y)=x^2 + y^2 +xy -1 = 0 ,$for all values of $x,y \in \mathbb R$. My attempt So i formed a function ...