Questions tagged [functions]
For elementary questions about functions, notation, properties, and operations such as function composition. Consider also using the (graphing-functions) tag.
34,514 questions
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Does the function $y=\frac{x-1}{x+1}$ have a name?
I am a student of Mathematics and currently going through Calculus course. I am sorry if it is not allowed to post here but I tried to search the answer online and could not be successful.
While ...
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2
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1
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Determine $A_k$ for $k \in (0, 1]$
The problem
Let $k>0$ and a set $A_k$ the set of all functions $f:\mathbb R\longrightarrow \mathbb R$ of the form $f(x)=ax^2+bx+c$ with $a,b,c \in \mathbb Z$ and which has the property that $f([0,1]...
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The graphs of f , f′ , and f′′ [closed]
The image shows the graphs of f, f` and f``. Determine each curve.
From my understanding, B=f,C=f′ and A=f′′.
C intersects the x-axis when B has a maximum, and A intersects the x-axis when C has a ...
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1
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1
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Doubt about the definition of Indexed Families of Sets [duplicate]
From what I've observed, a family is usually understood to be a collection of sets, where all the elements of this collection are themselves sets. For instance, the power set of a given set is a ...
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3
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0
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Bijection from irrationals to reals mapping rays to open sets
Is there a bijection $f:\mathbb R \to \mathbb Q^c$ such that for all $a\in \mathbb Q^c$, $f^{-1}((a, \infty)\cap\mathbb Q^c)$ is open in $\mathbb R$?
There is no bijection such that $f^{-1}((a,b))$ is ...
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1
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139
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+100
Finding a function for my research paper that satisfies the motivation and question in this post
Motivation: Suppose, we partition $\mathbb{R}$ into sets $A$ and $B$ with a positive measure in each non-empty, open interval. I want a simple example of a piece-wise function $f:\mathbb{R} \to \...
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Parameter α for integer-valued rational function [closed]
Всем привет! Я сформулировал следующую гипотезу которую назвал своим именем "Гипотезой Владислава". Она касается целочисленн��сти значений дробно-рациональной функции.
Гипотеза Владислава: ...
-1
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2
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57
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I am confused with an example about functions in Mendelson's Topology book. [closed]
Could somebody explain this example since I don't understand it.
Let $f: \mathbb{R} \to \mathbb{R} ; f(x)=x^2-x-2.$
If Z is the open interval $(-1,1)$, then $f(Z) = (- \frac{9}{4},0) \cup\{- \frac{...
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1
vote
1
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Decreasing bijections of dense uncountable subsets of $\mathbb R$
If $A\subseteq \mathbb R$ has $|A| = |\mathbb R|$ and $A$ is a dense aubset of $[a,b]$ ($a,b$ possibly infinite), then is there some $c$ (possibly infinite) with $a< c\leq b$ and a bijection $f:A\...
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4
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2
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361
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Approximating the Exponential Function Using Functions Asymptotically Insensitive to Scale
I am looking for a concrete formula for a sequence $f_n : \mathbb{R} \to \mathbb{R}$ of functions, as simple as possible, such that :
$f_n(x) \to e^x$ as $n \to \infty$ holds for every $x \in \mathbb{...
- 3,156
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0
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If $f(x+h)-f(x)-f'(x)(h) = O(h^2)$, what can we say about $f$? [closed]
If $$f(x+h)-f(x)-f'(x)(h) = O(h^2),$$ $f$ is differentiable but also a bit more than just differentiable. What kind of functions satisfy this property? Do they have a name?
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What function grows slower than any exponential but faster than "most" sub-exponentials?
I'm looking for a function $f \colon \mathbb{N} \to \mathbb{N}$ (or $\mathbb{R}^+ \to \mathbb{R}^+$) that satisfies:
Sub-exponential growth: For every $a > c1$ for some positive c1, $f(n) = o(a^n)$...
0
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1
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42
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Tricks to shorten a function with excessively many input variables. Can one variable be a set of variables?
Say I have the expression
\begin{equation}
f(x_1,\dots,x_n,y_1,\dots,y_m,z_1,\dots,z_k,r_1,\dots,r_d,t) = f(x_1,\dots,x_n,y_1,\dots,y_m,z_1,\dots,z_k,r_1,\dots,r_d)g(t),
\end{equation}
Could one have ...
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1
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56
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Function problem [closed]
Q. Let $f$ and $g$ be increasing and decreasing functions respectively from $[0, \infty)$ to $[0, \infty)$. Let $h(x) = f(g(x))$. If $h(0) = 0 $, then $h(x)$ is
So here my first thought is to ...
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0
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1
answer
80
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Concatenating $x^{\frac{1}{n}}$ with $1$
As a technical detail in my work, I need a concrete formula for a sequence of functions $f_n:[0, \infty) \to (a, \infty)$, as simple as possible, that satisfies all of the following conditions :
$f_n(...
- 3,156