You are making things more difficult than necessary in your effort to find the range. It is not really necessary to yield an inverse (as you seem to do). You could do it in simple steps:
- range of
is 
- range of
is 
- range of
is 
Expii
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Finding the Domain of a Function, Algebraically - Expii
How can values not be in the domain? Values not included in domain are values that will "break" the function. For example, values that would put negative numbers in square roots or a 0 in a denominator would not be included in a function's domain.
CK-12 Foundation
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Flexi answers - How to solve for domain algebraically? | CK-12 Foundation
September 11, 2025 - To solve for the domain algebraically, you need to identify the values of the independent variable (usually denoted as "x") for which the function is defined. The domain represents the set of all possible input values for which the function produces a valid output.
Videos
Cool Math
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Finding the Domain of a Function
OK, so suppose we don't have the graph of a function to look at like in the last section... ... So, we'll just be doing domains on these -- which is really where the action is anyway.
Mathway
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Find the Domain Calculator
Algebra · Domain of a Function Calculator · Step 1: Enter the Function you want to domain into the editor. The domain calculator allows you to take a simple or complex function and find the domain in both interval and set notation instantly. Step 2: Click the ·
Mathematics LibreTexts
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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.
Top answer 1 of 2
2
You are making things more difficult than necessary in your effort to find the range. It is not really necessary to yield an inverse (as you seem to do). You could do it in simple steps:
- range of is
- range of is
- range of is
2 of 2
1
I don't fully follow what you are doing to determine the range. In any case, when you have:
The LHS is a square and thus always positive, this inequality is satisfied for all 
...
In the formula:
the range of the monotonically increasing part 
is (clearly) 
, which means the denominator is monotonically decreasing with a maximum in 
, namely 
. For 
, 
but since 
for all 
, the range is: 
.
Alternatively:
So:
For the domain of:
You need:
For the range (given the domain as above):
Khan Academy
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Determine the domain of functions (practice)
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Wikihow
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7 Ways to Find the Domain of a Function - wikiHow
Learn the definition of the domain. The domain is defined as the set of input values for which the function produces an output value.[1] X Research source In other words, the domain is the full set of x-values that can be plugged into a function to produce a y-value.
Published July 18, 2024 Views 1K
YouTube
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❖ Finding the Domain of a Function Algebraically (No graph!) ❖ - YouTube
Finding the Domain of a Function Algebraically - Step-by-Step Examples!Description: In this video, I walk through finding the domain of a function algebraica...
Published July 13, 2010
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
CK-12 Foundation
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Flexi answers - How do you find the domain of a function algebraically? | CK-12 Foundation
September 4, 2024 - The domain of a function in the algebraic context is the set of input or argument values for which the function is defined. To find the domain of a function algebraically, perform the following steps: Steps To Find the Domain of a Function Algebraically Identify the Function Type: Different types of functions have different rules for their domains.
Reddit
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r/learnmath on Reddit: How do you find the range of a function algebraically
April 10, 2023 -
In every first pages of a calculus book, it talks about the domain and range of a function, domain is something I know how to deal with but range even though I understand it I don't how to find it systematically like the domain where you just say (pretend like e is the "belong to" symbol and 00 is infinity): f(x) = sqrt(4-x)
Df = { x e R / 4-x >= 0 } and you just solve the inequality and you get this ]-00,4].
I heard that you need to write x as a function of y but when I want to do it for polynomials or any other functions, I don't how to manipulate the terms.
Any help ??
Quora
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How to find the domain of a function algebraically - Quora
Answer (1 of 3): Domain is not the same as Domain. A) Domain is the set (say Da as subset R, their members are x) on which a formula F(x) is applicable. An assesment of (Da, F) specifies one function fa(x) B) But we can have im mind other function fb specified by (Db, F) where Db is subset od Da...
Varsity Tutors
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How to find the domain of a function - Algebra 1
We are given the function: To find the domain, first, know that you can't take the square root of a negative number. It turns out that the minimum number you can take the square root of is zero. Any number above zero, everything is good. Therefore, can equal 0 or above.
Symbolab
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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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BEST explanation how to determine domain algebraically - YouTube
👉 Learn about every thing you need to know to understand the domain and range of functions. We will look at functions represented as equations, tables, map...
Published October 4, 2016
Lumen Learning
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Find the domain of a function defined by an equation | College 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.
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 :)
Top answer 1 of 4
4
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 )
2 of 4
2
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.
Del Mar College
delmar.edu › offices › math › mlc › _resources › finding-the-domain-and-range-c.pdf pdf
East Campus, CB 117 Math Learning Center West Campus, HS1 203 361-698-1579
2. Algebraically: There is no set way to find the range algebraically. However, one strategy · that works most of the time is to find the domain of the inverse function (if it exists). First, swap the x and y variables everywhere they appear in the equation and then solve for y.
YouTube
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How to determine the domain of algebraic functions (examples) | Functions | Algebra I | Khan Academy - YouTube
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-functions/alg...
Published May 27, 2015