The best way to find the domain of a function is to find the values of x that are not in the domain and throw those values away. Once you've done that, whatever values of x are left give the domain. So you want to identify bad values of x and throw them away. What is a bad value of x? It's a value of x that causes some kind of problem. Common problems include: zero in the denominator of a fraction; a negative number under a square root; a nonpositive number inside a logarithm. Once you've identified all of the bad values of x and thrown them away, then the domain is everything that's left. === But what would I do in the case that have I something that isn't a fraction, like this: x + 2 = 1 + sqrt(2 + x) This doesn't make sense. That's an equation. It only makes sense to talk about domains of functions, not equations. or x - sqrt(2 - x) Three steps: Identify all of the bad values of x. Throw away those bad values. Everything that's left is the domain. So, what are the bad values of x here? Answer from zifyoip on reddit.com
Purplemath
purplemath.com › modules › rtnldefs.htm
Easily find the domains of rational expressions | Purplemath
Rational expresions (polynomial fractions) have variables in their denominators. Their domains are wherever those denominators are *not* equal to zero.
University of Kentucky
ms.uky.edu › ma109 › studentguide › sec-domainformula.html
Domain from a Formula
Variable in the denominator of a fraction: Set the denominator equal to 0 and solve. The domain is everything except that number. Square root of a variable in the denominator of a fraction: Set the inside of the square root strictly greater than 0 and solve. No square roots of variables or ...
[High School Math] How to find the Domain of something that isn't a fraction.
The best way to find the domain of a function is to find the values of x that are not in the domain and throw those values away. Once you've done that, whatever values of x are left give the domain. So you want to identify bad values of x and throw them away. What is a bad value of x? It's a value of x that causes some kind of problem. Common problems include: zero in the denominator of a fraction; a negative number under a square root; a nonpositive number inside a logarithm. Once you've identified all of the bad values of x and thrown them away, then the domain is everything that's left. === But what would I do in the case that have I something that isn't a fraction, like this: x + 2 = 1 + sqrt(2 + x) This doesn't make sense. That's an equation. It only makes sense to talk about domains of functions, not equations. or x - sqrt(2 - x) Three steps: Identify all of the bad values of x. Throw away those bad values. Everything that's left is the domain. So, what are the bad values of x here? More on reddit.com
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October 26, 2013Finding Domain of Functions: Do you only solve the top expression of a radical function when it has square root in the numerator?
If you’re working with the reals: You can’t take the square root of a negative number, or raise it to any other non-integer power. You can’t divide by zero A “find the domain” question boils down to finding all of of these possible values that would lead to one of these two things and excluding them from from the domain. More on reddit.com
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July 26, 2022algebra precalculus - How can I get the domain of a fraction under a square root? - Mathematics Stack Exchange
I can find the domain of a fraction function under a square root through drawing the function on graph. Yet, I seem to not be able to find it algebrically. To be precise, I want to find the domain of More on math.stackexchange.com
Finding domain of Rational function
So, if there are no values of x that make the denominator vanish, what can you conclude? More on reddit.com
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January 28, 2024Videos
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Sciencing
sciencing.com › domain-fraction-8479637
How To Find The Domain Of A Fraction - Sciencing
August 30, 2022 - Set up an algebra problem to isolate the variable in more complicated fractions. For example: To find the domain of 1/(x^2 -1), set up an algebra problem to find the values of x that would cause the denominator to equal 0.
Reddit
reddit.com › r/homeworkhelp › [high school math] how to find the domain of something that isn't a fraction.
r/HomeworkHelp on Reddit: [High School Math] How to find the Domain of something that isn't a fraction.
October 26, 2013 -
I know that the general process of finding the Domain of an expression (when it is a fraction) is merely that the denominator can't equal zero, so in the case of something like:
1/x + 3
It just becomes a matter of solving x + 3 = 0.
But what would I do in the case that have I something that isn't a fraction, like this:
x + 2 = 1 + sqrt(2 + x)
or x - sqrt(2 - x)
Top answer 1 of 3
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The best way to find the domain of a function is to find the values of x that are not in the domain and throw those values away. Once you've done that, whatever values of x are left give the domain. So you want to identify bad values of x and throw them away. What is a bad value of x? It's a value of x that causes some kind of problem. Common problems include: zero in the denominator of a fraction; a negative number under a square root; a nonpositive number inside a logarithm. Once you've identified all of the bad values of x and thrown them away, then the domain is everything that's left. === But what would I do in the case that have I something that isn't a fraction, like this: x + 2 = 1 + sqrt(2 + x) This doesn't make sense. That's an equation. It only makes sense to talk about domains of functions, not equations. or x - sqrt(2 - x) Three steps: Identify all of the bad values of x. Throw away those bad values. Everything that's left is the domain. So, what are the bad values of x here?
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Basically, you're looking for what won't give a valid output. That's why fractions are easy; as you said, you know in your first example that x can't equal -3, otherwise you're good to go. I'm assuming you want the domain that gives you real numbers as answers, i.e. imaginary number are a no go. In the case of a square root function, what are the conditions that give you a valid output? Say we have f(x) = sqrt(x - 10) and we want to know the domain. A square root is valid as long as you give it a non-negative number (i.e. you can take a square root of zero and above). So then your domain is x - 10 >= 0 And you can just rearrange it algebraically from there to get your domain for x.
Varsity Tutors
varsitytutors.com › home › domain and range of rational functions
Domain and Range of Rational Functions
Finding q(x)=0 gives domain restrictions; solving y·q(x)−p(x)=0 and analyzing behavior gives range restrictions. Domain excludes values where q(x)=0. Domain:All real numbers except where $q(x) = 0$ Range:All real numbers except values y with no solution to y·q(x)−p(x)=0 ·
Cuemath
cuemath.com › calculus › rational-function
Rational Function - Graph, Domain, Range, Asymptotes
Set of all real numbers other than the values of x mentioned in the last step is the domain. Example: Find the domain of f(x) = (2x + 1) / (3x - 2). ... We set the denominator not equal to zero.
Study.com
study.com › skill › learn › how-to-find-the-domain-of-a-fractional-function-involving-radicals-explanation.html
How to Find the Domain of a Fractional Function Involving Radicals | Precalculus | Study.com
May 20, 2021 - We have a radical which has an even degree (it is a square root). So we need everything underneath the radical to be non-negative. We can find this domain by setting everything underneath the radical greater than or equal to zero.
Mathematics LibreTexts
math.libretexts.org › bookshelves › applied mathematics › developmental math (nroc) › 17: functions › 17.2: using functions
17.2.3: Finding Domain and Range - Mathematics LibreTexts
December 15, 2024 - The other is the line \(\ y=1\), which provides a restriction to the range. In this case, there are no values of \(\ x\) for which \(\ f(x)=1\). So, the range for this function is all real numbers except 1. Finding the domain and range of different functions is often a matter of asking yourself, what values can this function not have?
Wyzant
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Domain and range of fraction | Wyzant Ask An Expert
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Reddit
reddit.com › r/learnmath › finding domain of functions: do you only solve the top expression of a radical function when it has square root in the numerator?
r/learnmath on Reddit: Finding Domain of Functions: Do you only solve the top expression of a radical function when it has square root in the numerator?
July 26, 2022 -
I'm learning to find the domain of functions. I've noticed, iirc, that the top expression seems to be ignored and only the denominator is solved to find the domain. It's not until there is a square root in the numerator that the top expression is solved for in order to be included in the domain. What is the reasoning for this if that's the case?
Top answer 1 of 2
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If you’re working with the reals: You can’t take the square root of a negative number, or raise it to any other non-integer power. You can’t divide by zero A “find the domain” question boils down to finding all of of these possible values that would lead to one of these two things and excluding them from from the domain.
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If the numerator is a polynomial, it accepts all inputs. However, you should factor it if possible to see if it shares any common factors with the denominator.
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I usually start by assuming the domain is all real numbers, then removing the values of $x$ that don't make sense. What remains is the domain. In your case, if $x=0$ then you are dividing by zero. That's bad, so remove $x=0$ from the domain. What else can go wrong? Taking the square root of a negative number will cause problems (unless you're working in the complex numbers). So figure out when is $1 + \frac{1}{x} < 0$. All those values of $x$ are not in the domain.
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Hint:
Basically, the conditions are $$x\ne 0\quad\text{and}\quad 1+\frac 1x=\frac{x+1}x\ge 0. $$ Now the sign of the fraction is the sign of the product $x(x+1)$, and you have a theorem about the sign of a quadratic polynomial…
Wikipedia
en.wikipedia.org › wiki › Continued_fraction
Continued fraction - Wikipedia
5 days ago - The story of continued fractions begins with the Euclidean algorithm, a procedure for finding the greatest common divisor of two natural numbers m and n. That algorithm introduced the idea of dividing to extract a new remainder – and then dividing by the new remainder repeatedly.
YouTube
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Domain of a function with a fraction | Easy - YouTube
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. Fo...
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.
CalculatorSoup
calculatorsoup.com › calculators › math › math-equation-solver.php
Math Equation Solver | Order of Operations
If you want an entry such as 1/2 to be treated as a fraction then enter it as (1/2). For example, in the equation 4 divided by ½ you must enter it as 4/(1/2). Then the division 1/2 = 0.5 is performed first and 4/0.5 = 8 is performed last.
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
When finding the domain of a fractional function, you must exclude all the x-values that make the denominator equal to zero, because you can never divide by zero.[3] X Research source So, write the denominator as an equation and set it equal ...
Published July 18, 2024 Views 1K
Quora
quora.com › How-do-you-find-the-domain-of-a-fractional-function
How to find the domain of a fractional function - Quora
Answer (1 of 4): Strictly speaking, the domain and codomain are parts of the definition of the function so questions like this are incomplete. But of course, the problem would be trivial if the domain were specified. (This paragraph is my only reason for answering as David Joyce’s answer is other...
Dhgate
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A Step-by-Step Guide to Finding the Domain of Fractional ...
1 month ago - Find expert-backed shopping guides and top product picks from DHgate. Make smarter decisions with curated insights tailored for international buyers.
Danville
danville.edu › sites › default › files › assets › files › Math Lab › Finding the Domain of Functions.pdf pdf
Finding Domain for Functions
SOLUTION: Since this is a linear polynomial, the domain is (−∞, ∞). PRECALCULUS TUTORIALS · Rational Functions · -A rational function is a function that contains variables in the denominator as well as the · numerator. Below are a few examples of rational functions. 𝑓(𝑥) = 2 · 𝑥−1 , 𝑓(𝑥) = 2𝑥−3 · 3𝑥−2 , 𝑓(𝑥) = 2𝑥2 −3𝑥+ 1 · 𝑥 · -It may be tempting to think that every function that contains fractions is rational, but this ·