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 ) Answer from Il_Valentino on reddit.com
Mathematics LibreTexts
math.libretexts.org › bookshelves › algebra › college algebra 1e (openstax) › 3: functions
3.3: Domain and Range - Mathematics LibreTexts
October 6, 2021 - If there is a denominator in the function’s formula, set the denominator equal to zero and solve for x . If the function’s formula contains an even root, set the radicand greater than or equal to 0, and then solve.
Mathway
mathway.com › Calculator › find-the-domain
Find the Domain Calculator
The domain calculator allows you to take a simple or complex function and find the domain in both interval and set notation instantly.
How do you find range and domain in general?
Domain is the set of possible X values in a function. Range is the set of possible Y values in a function. To find the domain, set the denominator equal to zero and then solve for X. Whatever X is is what CANNOT be in the domain. For example: 1/x, the domain is all real numbers except 0 because the denominator cannot be equal to zero. (Cannot divide by zero.) And easier, if there is no denominator and no square roots or anything like that, you know the domain is all real numbers. The range is easier to decipher by graphing. But it’s all possible Y values of a function More on reddit.com
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November 1, 2021Finding domain of a function
To find the domain of a function, the denominator can't equal 0, so set the denominator equal to 0 in order to find the "bad" x-values. √(3-2x) - 2 = 0 Add 2 to both sides. √(3-2x) = 2 Square both sides (to eliminate the root). 3 - 2x = 4 Subtract 3 from both sides. -2x = 1 Divide both sides by -2. x = -1/2 So, what this means is that x = -1/2 is NOT part of the domain of g(x) because plugging in x = -1/2 would give you 0 in the denominator. Now, because there's also a square root, the expression inside the root must be greater than (or equal to) 0. So let's set the expression inside the root greater than or equal to 0. 3 - 2x ≥ 0 Subtract 3 from both sides. -2x ≥ -3 Divide both sides by -2. (Remember that dividing by a negative flips the inequality symbol.) x ≤ 3/2 This means that the domain of g(x) is all x-values that are smaller than 3/2... excluding x = -1/2 since we found out above that this would give us 0 in the denominator. Therefore, the domain of g(x) is ... {x|x ≤ 3/2 and x ≠ -1/2} More on reddit.com
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July 12, 2019How 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, 2022Finding the domain of a function
You look for operations that are restricted, not allowed for all real numbers.
For instance, if there is a division, you know that you can't divide by 0. Therefore any x is excluded that makes the denominator 0.
If there's a square root, any x is excluded that would cause you to take the square root of a negative number.
So let's look at your function ,f(x) = x^2 - 1
Is there any real number that can't be squared? No. So x^2 exists for all real numbers.
Is there any real number you can't subtract 1 from? No. So x^2 - 1 exists for all real numbers. The domain is all real numbers.
More on reddit.com 9
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June 29, 2020What is a function domain?
The domain of a function is the set of all input values for which the function is defined. It is the set of all values that can be inserted into the function and produce a valid output.
symbolab.com
symbolab.com › solutions › functions & line calculator › functions domain calculator
Functions Domain Calculator
What's a function domain example?
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.
symbolab.com
symbolab.com › solutions › functions & line calculator › functions domain calculator
Functions Domain Calculator
Can I find the domain of a function with a calculator?
Yes. You can use a graphing calculator to calculate domain by plotting the function. There are also a variety of domain and range calculators online. Simply input your function to find the domain, which is a set of x-values that will successfully generate y-values.
wikihow.com
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7 Ways to Find the Domain of a Function - wikiHow
Videos
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.
Pressbooks
ecampusontario.pressbooks.pub › math3080prep › chapter › 2-2-finding-the-domain-of-a-function-defined-by-an-equation
2.2 Finding the Domain of a Function Defined by an Equation – Math 3080 Preparation
February 1, 2022 - If there is a denominator in the function’s formula, set the denominator equal to zero and solve for [latex]x[/latex]. If the function’s formula contains an even root, set the radicand greater than or equal to 0, and then solve.
Cuemath
cuemath.com › calculus › domain-and-range-of-a-function
Domain and Range - From Graph | How to Find Domain and Range of a Function?
Example: Find the domain and range of the function f(x) = |6 - x|. Domain: The domain of the function is the set ℝ. ... A square root function is of the form f(x) = √(ax+b). We know that the square root of a negative number is not defined.
Wikihow
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7 Ways to Find the Domain of a Function - wikiHow
A function with a fraction with a variable in the denominator. To find the domain of this type of function, set the bottom equal to zero and exclude the x value you find when you solve the equation.
Published July 18, 2024 Views 1K
Symbolab
symbolab.com › solutions › functions & line calculator › functions domain calculator
Functions Domain Calculator
It is the set of all values that ... of a function, consider any restrictions on the input values that would make the function undefined, including dividing by zero, taking the square root of a negative number, or taking the logarithm of a negative number....
YouTube
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How To Find The Domain of a Function - Radicals, Fractions & Square Roots - Interval Notation - YouTube
This algebra video tutorial explains how to find the domain of a function that contains radicals, fractions, and square roots in the denominator using interv...
Published September 8, 2017 Views 2M
Khan Academy
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Determine the domain of functions (practice)
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Khan Academy
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How to find the domain of a function (video)
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YouTube
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How to Find the Domain of a Function - YouTube
This algebra math tutorial explains how to find the domain of polynomial functions, rational functions, radical functions, square root functions, and functio...
Published April 15, 2024
Mathematics LibreTexts
math.libretexts.org › bookshelves › applied mathematics › calculus for business and social sciences corequisite workbook (dominguez, martinez, and saykali) › 4: functions
4.7: Domain and Range of a Function - Mathematics LibreTexts
July 18, 2022 - Any value can be chosen for \(z\), so the domain of the function is all real numbers, or as written in interval notation, is: \(D:(−\infty , \infty )\) To find the range, examine inside the absolute value symbols.
YouTube
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How to Find the Domain of Any Function (NancyPi) - YouTube
MIT grad shows a surefire way to find the domain of any function. To skip ahead: 1) For POLYNOMIAL only, skip to time 0:45. 2) For FRACTION only, skip to tim...
Published May 15, 2018
BYJUS
byjus.com › maths › domain-codomain-range-functions
Domain Range and Codomain Of A Function
August 17, 2022 - However, we can get the domain ... method of finding the range of a function, say y = f(x), is to express x as g(y) and identify the domain set for g(y)....
IntMath
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Domain and Range of a Function
After finishing this lesson head over to our interactive calculator to help you find the Domain and Range of a Fuction. ... The domain of this function is `x ≥ −4`, since x cannot be less than ` −4`. To see why, try out some numbers less than `−4` (like ` −5` or ` −10`) and some more than `−4` (like ` −2` or `8`) in your calculator.
GeeksforGeeks
geeksforgeeks.org › mathematics › domain-and-range-of-function
Domain and Range | How to Find Domain and Range of a Function - GeeksforGeeks
After taking all the steps discussed above the set of numbers left with us is considered the domain of a function. Solved Example: Find the domain of f(x) = 1/(x2 - 1)
Published October 11, 2022
Lumen Learning
courses.lumenlearning.com › intermediatealgebra › chapter › restricting-the-domain
Domain Restrictions | Intermediate Algebra
Since there is an even root, exclude any real numbers that result in a negative number in the radicand. Set the radicand greater than or equal to zero and solve for [latex]x[/latex]. The solution(s) are the domain of the function. If possible, write the answer in interval form.
Lumen Learning
courses.lumenlearning.com › waymakercollegealgebra › chapter › find-domain-and-range-from-a-graph
Determine Domain and Range from a Graph | College Algebra
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the [latex]x[/latex]-axis. The range is the set of possible output values, which are shown ...
Reddit
reddit.com › r/learnmath › how do you find range and domain in general?
How do you find range and domain in general? : r/learnmath
November 1, 2021 - Domain is the set of possible X values in a function. Range is the set of possible Y values in a function. To find the domain, set the denominator equal to zero and then solve for X.
University of Sydney
sydney.edu.au › content › dam › students › documents › mathematics-learning-centre › functions-domain-and-range.pdf pdf
Mathematics Learning Centre Functions: The domain and range Jackie Nicholas
The vertex of the function is at (1, 1) and therfore ... We sometimes give the rule y = f(x) along with the domain of definition.