Mathematics LibreTexts
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3.3: Domain and Range - Mathematics LibreTexts
October 6, 2021 - In interval form, the domain of f is \((−\infty,\infty)\). ... Identify the input values. Identify any restrictions on the input. If there is a denominator in the function’s formula, set the denominator equal to zero and solve for x .
Mathway
mathway.com › Calculator › find-the-domain
Find the Domain Calculator
The domain calculator allows to find the domain of functions and expressions and receive results in interval notation and set notation.
How do you find the domain of a function without graphing it?
technically the domain is part of the definition of a function and you can have different domains with the same functional equation for example we can have: f: R- to R with f(x)=1/x and g: R+ to R with g(x)=1/x so if I tell you h(x)=1/x you have no information about the domain however in applied math people usually just use a functional equation to represent a function and implicitely set the domain as the biggest possible subset within the real numbers so in the case of our example the function h can accept any real number except 0, hence its biggest possible domain is R \ {0} such that: h: R \ {0} to R with h(x)=1/x so the general strategy is to look for problematic values that cause division by zero or similar issues (like square root from negative numbers) and to exclude them consider for example: f(x)=sqrt(1-x2 ) in this case the problematic values are all x such that: 1-x2 <0 iff 1 < x2 iff 1 < |x| so the domain of f is all real numbers except those with an absolute values bigger than 1, which means only values between -1 and 1 are allowed: f: [-1, 1] to R, f(x)=sqrt(1-x2 ) More on reddit.com
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August 28, 2022Real number symbol (UTF-8: ℝ) in XeTeX
How can I get the 'real number' sign (something like \mathbb{R} with the amssymb package in LaTeX) in XeTeX? More on tex.stackexchange.com
calculus - Finding a function's domain from the function's formula - Mathematics Stack Exchange
The answer for $g(t)$ makes some sense because, without any specification otherwise, it seems reasonable to me to assume that the domain is infinite. However, I don't understand the meaning of the answer to $f(x)$, nor do I understand how it can depend on the formula of the function. More on math.stackexchange.com
How to write the domain and range of a function?
The [a, b] is closed interval notation. It tells us the endpoint a and b are closed. The { } is called set notation. You don’t really need to worry about it for now, but we can write [a,b] as the set. { x is real number | a <= x <= b} When infinity is in the domain, we can’t use closed interval. It has to be opened. And open interval is written as (a,b). We can have one endpoint be opened and the other be closed. It would be [a, b) or (b, a]. In your post it should be [0, infinity) The second notation tells us that the domain is all real numbers, excluding 0. Generally you should be allowed to just write that not using set notation. More on reddit.com
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September 5, 2020Videos
17:31
How to Find the Domain of a Function - YouTube
Find the Domain of a Function (Precalculus) Given Equation (4 ...
12:40
How to Find the Domain of Any Function (NancyPi) - YouTube
18:45
How To Find The Domain of a Function - Radicals, Fractions & Square ...
Examples finding the domain of functions (video)
Find the Domain of the Function Given the Equation
set of "input" or argument values for which a function is defined
Wikipedia
en.wikipedia.org › wiki › Domain_of_a_function
Domain of a function - Wikipedia
2 days ago - In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by ... {\displaystyle \operatorname {dom} f} , where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be".
Reddit
reddit.com › r/learnmath › how do you find the domain of a function without graphing it?
r/learnmath on Reddit: How do you find the domain of a function without graphing it?
August 28, 2022 -
I've been looking at all sorts of tutorials and walkthroughs on youtube and math-online, but I really can't get it
Please explain to me like I'm the idiot I am :)
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technically the domain is part of the definition of a function and you can have different domains with the same functional equation for example we can have: f: R- to R with f(x)=1/x and g: R+ to R with g(x)=1/x so if I tell you h(x)=1/x you have no information about the domain however in applied math people usually just use a functional equation to represent a function and implicitely set the domain as the biggest possible subset within the real numbers so in the case of our example the function h can accept any real number except 0, hence its biggest possible domain is R \ {0} such that: h: R \ {0} to R with h(x)=1/x so the general strategy is to look for problematic values that cause division by zero or similar issues (like square root from negative numbers) and to exclude them consider for example: f(x)=sqrt(1-x2 ) in this case the problematic values are all x such that: 1-x2 <0 iff 1 < x2 iff 1 < |x| so the domain of f is all real numbers except those with an absolute values bigger than 1, which means only values between -1 and 1 are allowed: f: [-1, 1] to R, f(x)=sqrt(1-x2 )
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For most polynomials, you determine if there is a point that does not exists. For example, y = x/(x-1), you than see when x =1, you get 1/0 which doesn't exist. For y = tan(x), if you know your trig, this is sin(x)/cos(x), so try to solve for when cosx = 0. When x = pi/2, you get 1/0 again which dies not exist. Over time you will learn the domain of specific functions. For example, y= ln(x), the domain is x >0. This is something you either memorize or once you understand the application of ln(x) you intuitively know the domain.
University of Kentucky
ms.uky.edu › ma109 › studentguide › sec-domainformula.html
Domain from a Formula
Now, remember that we figured out where the denominator is equal to 0, which is where the problem is. However, the domain is everything that isn't a problem, so our domain will be everything except 1. That means we need to include all the numbers that are bigger than 1 and all the numbers that are less than 1, but just not 1 itself.
Lumen Learning
courses.lumenlearning.com › intermediatealgebra › chapter › restricting-the-domain
Domain Restrictions | Intermediate Algebra
In interval form, the domain of [latex]f[/latex] is [latex]\left(-\infty ,\infty \right)[/latex]. Identify the input values. Identify any restrictions on the input. If there is a denominator in the function’s formula, set the denominator equal to zero and solve for [latex]x[/latex] .
Cuemath
cuemath.com › calculus › modulus-function
Modulus Function - Formula, Graph, Properties, Domain, Range
If f(x) is a modulus function, ... then the function takes minus of the actual value 'x'. We can apply the modulus function f(x) = |x| to any real number. i.e., its input can be any real number and hence its domain is the set ...
Cuemath
cuemath.com › calculus › domain-and-range-of-a-function
Domain and Range - From Graph | How to Find Domain and Range of a Function?
The domain is the set of all the input values of a function and the range is the possible output given by the function. Domain→ Function →Range. If there exists a function f: A →B such that every element of set A is mapped to elements ...
GeeksforGeeks
geeksforgeeks.org › mathematics › domain-and-range-of-function
Domain and Range | How to Find Domain and Range of a Function - GeeksforGeeks
Domain: All non-negative real numbers (x ≥ 0), because you cannot take the square root of a negative number in the set of real numbers. Check the Function's Expression: Start by analyzing the function’s formula to identify the type of function (e.g., quadratic, square root, rational, etc.)
Published October 11, 2022
Lumen Learning
courses.lumenlearning.com › waymakercollegealgebra › chapter › find-domain-and-range-from-a-graph
Determine Domain and Range from a Graph | College Algebra
The output quantity is “thousands of barrels of oil per day,” which we represent with the variable [latex]b[/latex] for barrels. The graph may continue to the left and right beyond what is viewed, but based on the portion of the graph that is visible, we can determine the domain as [latex]1973\le t\le 2008[/latex] and the range as approximately [latex]180\le b\le 2010[/latex].
Lumen Learning
courses.lumenlearning.com › atd-sanjac-collegealgebra › chapter › find-the-domain-of-a-function-defined-by-an-equation
Find the domain of a function defined by an equation | College Algebra
Find the domain of the function: [latex]f\left(x\right)=5-x+{x}^{3}[/latex]. ... Identify the input values. Identify any restrictions on the input. If there is a denominator in the function’s formula, set the denominator equal to zero and solve for [latex]x[/latex] .
Symbolab
symbolab.com › solutions › functions & line calculator › functions domain calculator
Functions Domain Calculator
For the function f(x) = 1/x, the domain would be all real numbers except for x = 0 (x<0 or x>0), as division by zero is undefined.
Study.com
study.com › math › algebra
Domain & Range of a Function | Definition, Equation & Examples - Lesson | Study.com
January 11, 2013 - The domain of a function is the set of all input values that the function is defined upon. It is all of the values that can be substituted (plugged in) to the function itself such that the function remains defined. The range of a function is the set of all output values in which the function is defined.
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How about this?
\documentclass{article}
\usepackage{amssymb}
\begin{document}
\begin{tabular}{ll}
Plain-\TeX{}: & ${\rm I\!R}$\\
amssymb: & $\mathbb{R}$
\end{tabular}
\end{document}
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You should put your symbol format definitions in another TeX file; publications tend to have their own styles, and some may use bold Roman for fields like R instead of blackboard bold. You can swap nams.tex with aom.tex. I know, this is more common with LaTeX, but the principle still applies.
For example:
% paper.tex
\input nams.tex
$\realnumbers$ is connected.
% nams.tex
\def\realnumbers{\mathbb{R}}
% more definitions for the Notices.
% aom.tex
\def\realnumbers{\mathbf{R}}
% more definitions for the Annals.
Just change one line in paper.tex to submit to the Annals instead of the Notices.
Varsity Tutors
varsitytutors.com › algebra_1-help › how-to-find-the-domain-of-a-function
How to find the domain of a function - Algebra 1
The domain of a rational function is the set of all values of for which the denominator is not equal to 0 (the value of the numerator is irrelevant), so we set the denominator to 0 and solve for to find the excluded values.
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You're quite right; the book is using the term "domain" incorrectly. What they mean is "the greatest possible subset of the real numbers that could be used as the domain of a function whose values are given by this formula".
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As you say, the domain of a function is part of its definition. The "definitions" of $f$ and $g$, in the context of the question, are not definitions at all, but merely equations. I would reformulate the question as: what is the largest domain in $\mathbb{R}$ for which this equation defines a function?
Wikihow
wikihow.com › education and communications › studying › mathematics › 7 ways to find the domain of a function - wikihow
7 Ways to Find the Domain of a Function - wikiHow
The domain of a function is the set of input values (x) for which the function produces an output value (y).
Published July 18, 2024 Views 1K
Wolfram|Alpha
wolframalpha.com › calculators › domain-range-calculator
Domain and Range Calculator: Step-by-Step Solutions - Wolfram|Alpha
Informally, if a function is defined on some set, then we call that set the domain. The values taken by the function are collectively referred to as the range. For example, the function Start Power, Start base, x , base End,Start exponent, 2 , exponent End , Power Endx2 takes the reals (domain) to the non-negative reals (range).
Purplemath
purplemath.com › modules › fcns2.htm
Functions: Domain, domain on the range...🎶 | Purplemath
A function's domain is where the function lives, where it starts from; its range is where it travels, where it goes to. Just like the old cowboy song!
IntMath
intmath.com › home › introduction to geometry › 4a. domain and range of a function
Domain and Range of a Function
Simple explanation for domain and range. We learn the domain of a function is the set of possible x-values and the range is the resulting set of y-values.