What is the domain of the function $f(x)=sqrt[3]x^3-x$? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)When should the antiderivative of a rational function be defined as a piecewise function?Domain of this functionWhat is the domain of the inverse functionDomain of the function and its simplified expressionIs this interval in the domain?Showing that $sum_n=2^infty f(frac 1n)$ converges using the MVTWhat does it mean for a function to be continuous on its domain?Finding the domain of $sqrtx^2-7$Maximum domain of definition of some $ln$ and $sqrtx$ functionNo Derivability at 0+ point, why not including 0 in function domain
Significance of Cersei's obsession with elephants?
Multiple OR (||) Conditions in If Statement
SF book about people trapped in a series of worlds they imagine
If windows 7 doesn't support WSL, then what does Linux subsystem option mean?
Why should I vote and accept answers?
Are all finite dimensional hilbert spaces isomorphic to spaces with Euclidean norms?
Chinese Seal on silk painting - what does it mean?
Can a new player join a group only when a new campaign starts?
Should I use a zero-interest credit card for a large one-time purchase?
Dating a Former Employee
Chebyshev inequality in terms of RMS
Do any jurisdictions seriously consider reclassifying social media websites as publishers?
Do wooden building fires get hotter than 600°C?
How does the math work when buying airline miles?
How to tell that you are a giant?
How do I find out the mythology and history of my Fortress?
Is it possible for SQL statements to execute concurrently within a single session in SQL Server?
How fail-safe is nr as stop bytes?
What do you call the main part of a joke?
Should I follow up with an employee I believe overracted to a mistake I made?
Generate an RGB colour grid
Can anything be seen from the center of the Boötes void? How dark would it be?
Maximum summed subsequences with non-adjacent items
What is this clumpy 20-30cm high yellow-flowered plant?
What is the domain of the function $f(x)=sqrt[3]x^3-x$?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)When should the antiderivative of a rational function be defined as a piecewise function?Domain of this functionWhat is the domain of the inverse functionDomain of the function and its simplified expressionIs this interval in the domain?Showing that $sum_n=2^infty f(frac 1n)$ converges using the MVTWhat does it mean for a function to be continuous on its domain?Finding the domain of $sqrtx^2-7$Maximum domain of definition of some $ln$ and $sqrtx$ functionNo Derivability at 0+ point, why not including 0 in function domain
$begingroup$
Let $f$ be: $f(x) = sqrt[3]x^3 -x$, an exercise book asked for the domain of definition. Isn't it over $mathbb R$. The book solution stated $Df = [-1,0] cup [1, +infty[$
I don t get it. Can you explain?
calculus
edited Apr 14 at 18:18
Asaf Karagila♦
309k33441775
asked Apr 14 at 9:36
J.MohJ.Moh
695
$endgroup$
|
show 1 more comment
$begingroup$
Let $f$ be: $f(x) = sqrt[3]x^3 -x$, an exercise book asked for the domain of definition. Isn't it over $mathbb R$. The book solution stated $Df = [-1,0] cup [1, +infty[$
I don t get it. Can you explain?
calculus
edited Apr 14 at 18:18
Asaf Karagila♦
309k33441775
asked Apr 14 at 9:36
J.MohJ.Moh
695
$endgroup$
$begingroup$
It is $$x^3-xgeq 0$$
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:39
$begingroup$
I think it's better $D(f)=mathbb R$, but if $g(x)=(x^3-x)^frac13$ so $D(g)=x^3-x>0.$ All these a definition only.
$endgroup$
– Michael Rozenberg
Apr 14 at 9:42
$begingroup$
@Dr.SonnhardGraubner can you explain why?
$endgroup$
– J.Moh
Apr 14 at 9:46
$begingroup$
$$g(0)=0$$ dear Michael.
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:55
$begingroup$
Are you quite sure it wasn't $sqrtx^3-x$? Because the domain of $sqrt[3]x^3 -x$ is $Bbb R$.
$endgroup$
– TonyK
Apr 14 at 18:21
|
show 1 more comment
$begingroup$
Let $f$ be: $f(x) = sqrt[3]x^3 -x$, an exercise book asked for the domain of definition. Isn't it over $mathbb R$. The book solution stated $Df = [-1,0] cup [1, +infty[$
I don t get it. Can you explain?
calculus
edited Apr 14 at 18:18
Asaf Karagila♦
309k33441775
asked Apr 14 at 9:36
J.MohJ.Moh
695
$endgroup$
Let $f$ be: $f(x) = sqrt[3]x^3 -x$, an exercise book asked for the domain of definition. Isn't it over $mathbb R$. The book solution stated $Df = [-1,0] cup [1, +infty[$
I don t get it. Can you explain?
calculus
calculus
edited Apr 14 at 18:18
Asaf Karagila♦
309k33441775
asked Apr 14 at 9:36
J.MohJ.Moh
695
edited Apr 14 at 18:18
Asaf Karagila♦
309k33441775
asked Apr 14 at 9:36
J.MohJ.Moh
695
edited Apr 14 at 18:18
Asaf Karagila♦
309k33441775
edited Apr 14 at 18:18
Asaf Karagila♦
309k33441775
edited Apr 14 at 18:18
Asaf Karagila♦
309k33441775
309k33441775
asked Apr 14 at 9:36
J.MohJ.Moh
695
asked Apr 14 at 9:36
J.MohJ.Moh
695
asked Apr 14 at 9:36
J.MohJ.Moh
695
695
$begingroup$
It is $$x^3-xgeq 0$$
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:39
$begingroup$
I think it's better $D(f)=mathbb R$, but if $g(x)=(x^3-x)^frac13$ so $D(g)=x^3-x>0.$ All these a definition only.
$endgroup$
– Michael Rozenberg
Apr 14 at 9:42
$begingroup$
@Dr.SonnhardGraubner can you explain why?
$endgroup$
– J.Moh
Apr 14 at 9:46
$begingroup$
$$g(0)=0$$ dear Michael.
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:55
$begingroup$
Are you quite sure it wasn't $sqrtx^3-x$? Because the domain of $sqrt[3]x^3 -x$ is $Bbb R$.
$endgroup$
– TonyK
Apr 14 at 18:21
|
show 1 more comment
$begingroup$
It is $$x^3-xgeq 0$$
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:39
$begingroup$
I think it's better $D(f)=mathbb R$, but if $g(x)=(x^3-x)^frac13$ so $D(g)=x^3-x>0.$ All these a definition only.
$endgroup$
– Michael Rozenberg
Apr 14 at 9:42
$begingroup$
@Dr.SonnhardGraubner can you explain why?
$endgroup$
– J.Moh
Apr 14 at 9:46
$begingroup$
$$g(0)=0$$ dear Michael.
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:55
$begingroup$
Are you quite sure it wasn't $sqrtx^3-x$? Because the domain of $sqrt[3]x^3 -x$ is $Bbb R$.
$endgroup$
– TonyK
Apr 14 at 18:21
$begingroup$
It is $$x^3-xgeq 0$$
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:39
$begingroup$
It is $$x^3-xgeq 0$$
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:39
$begingroup$
I think it's better $D(f)=mathbb R$, but if $g(x)=(x^3-x)^frac13$ so $D(g)=x^3-x>0.$ All these a definition only.
$endgroup$
– Michael Rozenberg
Apr 14 at 9:42
$begingroup$
I think it's better $D(f)=mathbb R$, but if $g(x)=(x^3-x)^frac13$ so $D(g)=x^3-x>0.$ All these a definition only.
$endgroup$
– Michael Rozenberg
Apr 14 at 9:42
$begingroup$
@Dr.SonnhardGraubner can you explain why?
$endgroup$
– J.Moh
Apr 14 at 9:46
$begingroup$
@Dr.SonnhardGraubner can you explain why?
$endgroup$
– J.Moh
Apr 14 at 9:46
$begingroup$
$$g(0)=0$$ dear Michael.
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:55
$begingroup$
$$g(0)=0$$ dear Michael.
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:55
$begingroup$
Are you quite sure it wasn't $sqrtx^3-x$? Because the domain of $sqrt[3]x^3 -x$ is $Bbb R$.
$endgroup$
– TonyK
Apr 14 at 18:21
$begingroup$
Are you quite sure it wasn't $sqrtx^3-x$? Because the domain of $sqrt[3]x^3 -x$ is $Bbb R$.
$endgroup$
– TonyK
Apr 14 at 18:21
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
If your book reaches the domain $[-1,0]cup[1,+infty)$, it must be because the book only considers $sqrt[3]phantomX$ to be defined when the argument is a non-negative real.
Books (and people) differ in how they consider $sqrt[N]phantom X$ to be defined.
Some people find it okay to define odd roots on the entire real line -- after all, $xmapsto x^N$ is a bijection on $mathbb R$ when $N$ is positive odd, and every such bijection has a perfectly fine inverse.
Other people prefer to restrict these functions to non-negative reals, no matter what $N$ is -- partially to avoid creating a (confusing?) distinction between odd and even $N$, partially for more subtle reasons that unfortunately are not apparent when one first learns about roots.
(For even subtler reasons, one might even want to reserve the root notation to arguments that are strictly positive, such that $sqrt 0$ is considered undefined. It is somewhat rare to take that position consistently, though).
You'll just have to live with the fact that such questions cannot be answered without knowing which convention for the root sign is to be used. (Arguably it is bad form to let a find-the-domain-of-this-expression exercise depend on such choices, but that's purely the textbook's fault, of course).
answered Apr 14 at 9:57
Henning MakholmHenning Makholm
244k17312556
$endgroup$
$begingroup$
That s why I love computer scientists, they answer as if they re writing code ;) Thanks Henning! Perfect!
$endgroup$
– J.Moh
Apr 14 at 10:26
1
$begingroup$
@J.Moh: If every mathematics student learns programming, we would hardly see any of the silly mistakes arising from imprecision. I agree with Henning's last sentence and even say that such kind of questions are terrible because they encourage imprecision. Moreover, I personally think that we should define $sqrt[n]x$ for all real $x$ and odd natural number $n$, because $(mathbbR x ↦ x^n)$ is a bijection from $mathbbR$ to $mathbbR$, so its inverse exists. Similarly for non-negative real $x$ and even natural number $n$.
$endgroup$
– user21820
Apr 14 at 15:30
$begingroup$
@J.Moh: By the way, if you are satisfied with this answer, you can click the tick to accept it.
$endgroup$
– user21820
Apr 14 at 15:32
1
$begingroup$
I agree! I found refuge in math and programming since I could sense for the first time what honesty was.
$endgroup$
– J.Moh
Apr 14 at 15:35
$begingroup$
@user21820 I did
$endgroup$
– J.Moh
Apr 14 at 15:36
|
show 2 more comments
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3187198%2fwhat-is-the-domain-of-the-function-fx-sqrt3x3-x%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If your book reaches the domain $[-1,0]cup[1,+infty)$, it must be because the book only considers $sqrt[3]phantomX$ to be defined when the argument is a non-negative real.
Books (and people) differ in how they consider $sqrt[N]phantom X$ to be defined.
Some people find it okay to define odd roots on the entire real line -- after all, $xmapsto x^N$ is a bijection on $mathbb R$ when $N$ is positive odd, and every such bijection has a perfectly fine inverse.
Other people prefer to restrict these functions to non-negative reals, no matter what $N$ is -- partially to avoid creating a (confusing?) distinction between odd and even $N$, partially for more subtle reasons that unfortunately are not apparent when one first learns about roots.
(For even subtler reasons, one might even want to reserve the root notation to arguments that are strictly positive, such that $sqrt 0$ is considered undefined. It is somewhat rare to take that position consistently, though).
You'll just have to live with the fact that such questions cannot be answered without knowing which convention for the root sign is to be used. (Arguably it is bad form to let a find-the-domain-of-this-expression exercise depend on such choices, but that's purely the textbook's fault, of course).
answered Apr 14 at 9:57
Henning MakholmHenning Makholm
244k17312556
$endgroup$
$begingroup$
That s why I love computer scientists, they answer as if they re writing code ;) Thanks Henning! Perfect!
$endgroup$
– J.Moh
Apr 14 at 10:26
1
$begingroup$
@J.Moh: If every mathematics student learns programming, we would hardly see any of the silly mistakes arising from imprecision. I agree with Henning's last sentence and even say that such kind of questions are terrible because they encourage imprecision. Moreover, I personally think that we should define $sqrt[n]x$ for all real $x$ and odd natural number $n$, because $(mathbbR x ↦ x^n)$ is a bijection from $mathbbR$ to $mathbbR$, so its inverse exists. Similarly for non-negative real $x$ and even natural number $n$.
$endgroup$
– user21820
Apr 14 at 15:30
$begingroup$
@J.Moh: By the way, if you are satisfied with this answer, you can click the tick to accept it.
$endgroup$
– user21820
Apr 14 at 15:32
1
$begingroup$
I agree! I found refuge in math and programming since I could sense for the first time what honesty was.
$endgroup$
– J.Moh
Apr 14 at 15:35
$begingroup$
@user21820 I did
$endgroup$
– J.Moh
Apr 14 at 15:36
|
show 2 more comments
$begingroup$
If your book reaches the domain $[-1,0]cup[1,+infty)$, it must be because the book only considers $sqrt[3]phantomX$ to be defined when the argument is a non-negative real.
Books (and people) differ in how they consider $sqrt[N]phantom X$ to be defined.
Some people find it okay to define odd roots on the entire real line -- after all, $xmapsto x^N$ is a bijection on $mathbb R$ when $N$ is positive odd, and every such bijection has a perfectly fine inverse.
Other people prefer to restrict these functions to non-negative reals, no matter what $N$ is -- partially to avoid creating a (confusing?) distinction between odd and even $N$, partially for more subtle reasons that unfortunately are not apparent when one first learns about roots.
(For even subtler reasons, one might even want to reserve the root notation to arguments that are strictly positive, such that $sqrt 0$ is considered undefined. It is somewhat rare to take that position consistently, though).
You'll just have to live with the fact that such questions cannot be answered without knowing which convention for the root sign is to be used. (Arguably it is bad form to let a find-the-domain-of-this-expression exercise depend on such choices, but that's purely the textbook's fault, of course).
answered Apr 14 at 9:57
Henning MakholmHenning Makholm
244k17312556
$endgroup$
$begingroup$
That s why I love computer scientists, they answer as if they re writing code ;) Thanks Henning! Perfect!
$endgroup$
– J.Moh
Apr 14 at 10:26
1
$begingroup$
@J.Moh: If every mathematics student learns programming, we would hardly see any of the silly mistakes arising from imprecision. I agree with Henning's last sentence and even say that such kind of questions are terrible because they encourage imprecision. Moreover, I personally think that we should define $sqrt[n]x$ for all real $x$ and odd natural number $n$, because $(mathbbR x ↦ x^n)$ is a bijection from $mathbbR$ to $mathbbR$, so its inverse exists. Similarly for non-negative real $x$ and even natural number $n$.
$endgroup$
– user21820
Apr 14 at 15:30
$begingroup$
@J.Moh: By the way, if you are satisfied with this answer, you can click the tick to accept it.
$endgroup$
– user21820
Apr 14 at 15:32
1
$begingroup$
I agree! I found refuge in math and programming since I could sense for the first time what honesty was.
$endgroup$
– J.Moh
Apr 14 at 15:35
$begingroup$
@user21820 I did
$endgroup$
– J.Moh
Apr 14 at 15:36
|
show 2 more comments
$begingroup$
If your book reaches the domain $[-1,0]cup[1,+infty)$, it must be because the book only considers $sqrt[3]phantomX$ to be defined when the argument is a non-negative real.
Books (and people) differ in how they consider $sqrt[N]phantom X$ to be defined.
Some people find it okay to define odd roots on the entire real line -- after all, $xmapsto x^N$ is a bijection on $mathbb R$ when $N$ is positive odd, and every such bijection has a perfectly fine inverse.
Other people prefer to restrict these functions to non-negative reals, no matter what $N$ is -- partially to avoid creating a (confusing?) distinction between odd and even $N$, partially for more subtle reasons that unfortunately are not apparent when one first learns about roots.
(For even subtler reasons, one might even want to reserve the root notation to arguments that are strictly positive, such that $sqrt 0$ is considered undefined. It is somewhat rare to take that position consistently, though).
You'll just have to live with the fact that such questions cannot be answered without knowing which convention for the root sign is to be used. (Arguably it is bad form to let a find-the-domain-of-this-expression exercise depend on such choices, but that's purely the textbook's fault, of course).
answered Apr 14 at 9:57
Henning MakholmHenning Makholm
244k17312556
$endgroup$
If your book reaches the domain $[-1,0]cup[1,+infty)$, it must be because the book only considers $sqrt[3]phantomX$ to be defined when the argument is a non-negative real.
Books (and people) differ in how they consider $sqrt[N]phantom X$ to be defined.
Some people find it okay to define odd roots on the entire real line -- after all, $xmapsto x^N$ is a bijection on $mathbb R$ when $N$ is positive odd, and every such bijection has a perfectly fine inverse.
Other people prefer to restrict these functions to non-negative reals, no matter what $N$ is -- partially to avoid creating a (confusing?) distinction between odd and even $N$, partially for more subtle reasons that unfortunately are not apparent when one first learns about roots.
(For even subtler reasons, one might even want to reserve the root notation to arguments that are strictly positive, such that $sqrt 0$ is considered undefined. It is somewhat rare to take that position consistently, though).
You'll just have to live with the fact that such questions cannot be answered without knowing which convention for the root sign is to be used. (Arguably it is bad form to let a find-the-domain-of-this-expression exercise depend on such choices, but that's purely the textbook's fault, of course).
answered Apr 14 at 9:57
Henning MakholmHenning Makholm
244k17312556
edited Apr 14 at 10:03
answered Apr 14 at 9:57
Henning MakholmHenning Makholm
244k17312556
answered Apr 14 at 9:57
Henning MakholmHenning Makholm
244k17312556
answered Apr 14 at 9:57
Henning MakholmHenning Makholm
244k17312556
244k17312556
$begingroup$
That s why I love computer scientists, they answer as if they re writing code ;) Thanks Henning! Perfect!
$endgroup$
– J.Moh
Apr 14 at 10:26
1
$begingroup$
@J.Moh: If every mathematics student learns programming, we would hardly see any of the silly mistakes arising from imprecision. I agree with Henning's last sentence and even say that such kind of questions are terrible because they encourage imprecision. Moreover, I personally think that we should define $sqrt[n]x$ for all real $x$ and odd natural number $n$, because $(mathbbR x ↦ x^n)$ is a bijection from $mathbbR$ to $mathbbR$, so its inverse exists. Similarly for non-negative real $x$ and even natural number $n$.
$endgroup$
– user21820
Apr 14 at 15:30
$begingroup$
@J.Moh: By the way, if you are satisfied with this answer, you can click the tick to accept it.
$endgroup$
– user21820
Apr 14 at 15:32
1
$begingroup$
I agree! I found refuge in math and programming since I could sense for the first time what honesty was.
$endgroup$
– J.Moh
Apr 14 at 15:35
$begingroup$
@user21820 I did
$endgroup$
– J.Moh
Apr 14 at 15:36
|
show 2 more comments
$begingroup$
That s why I love computer scientists, they answer as if they re writing code ;) Thanks Henning! Perfect!
$endgroup$
– J.Moh
Apr 14 at 10:26
1
$begingroup$
@J.Moh: If every mathematics student learns programming, we would hardly see any of the silly mistakes arising from imprecision. I agree with Henning's last sentence and even say that such kind of questions are terrible because they encourage imprecision. Moreover, I personally think that we should define $sqrt[n]x$ for all real $x$ and odd natural number $n$, because $(mathbbR x ↦ x^n)$ is a bijection from $mathbbR$ to $mathbbR$, so its inverse exists. Similarly for non-negative real $x$ and even natural number $n$.
$endgroup$
– user21820
Apr 14 at 15:30
$begingroup$
@J.Moh: By the way, if you are satisfied with this answer, you can click the tick to accept it.
$endgroup$
– user21820
Apr 14 at 15:32
1
$begingroup$
I agree! I found refuge in math and programming since I could sense for the first time what honesty was.
$endgroup$
– J.Moh
Apr 14 at 15:35
$begingroup$
@user21820 I did
$endgroup$
– J.Moh
Apr 14 at 15:36
$begingroup$
That s why I love computer scientists, they answer as if they re writing code ;) Thanks Henning! Perfect!
$endgroup$
– J.Moh
Apr 14 at 10:26
$begingroup$
That s why I love computer scientists, they answer as if they re writing code ;) Thanks Henning! Perfect!
$endgroup$
– J.Moh
Apr 14 at 10:26
1
1
$begingroup$
@J.Moh: If every mathematics student learns programming, we would hardly see any of the silly mistakes arising from imprecision. I agree with Henning's last sentence and even say that such kind of questions are terrible because they encourage imprecision. Moreover, I personally think that we should define $sqrt[n]x$ for all real $x$ and odd natural number $n$, because $(mathbbR x ↦ x^n)$ is a bijection from $mathbbR$ to $mathbbR$, so its inverse exists. Similarly for non-negative real $x$ and even natural number $n$.
$endgroup$
– user21820
Apr 14 at 15:30
$begingroup$
@J.Moh: If every mathematics student learns programming, we would hardly see any of the silly mistakes arising from imprecision. I agree with Henning's last sentence and even say that such kind of questions are terrible because they encourage imprecision. Moreover, I personally think that we should define $sqrt[n]x$ for all real $x$ and odd natural number $n$, because $(mathbbR x ↦ x^n)$ is a bijection from $mathbbR$ to $mathbbR$, so its inverse exists. Similarly for non-negative real $x$ and even natural number $n$.
$endgroup$
– user21820
Apr 14 at 15:30
$begingroup$
@J.Moh: By the way, if you are satisfied with this answer, you can click the tick to accept it.
$endgroup$
– user21820
Apr 14 at 15:32
$begingroup$
@J.Moh: By the way, if you are satisfied with this answer, you can click the tick to accept it.
$endgroup$
– user21820
Apr 14 at 15:32
1
1
$begingroup$
I agree! I found refuge in math and programming since I could sense for the first time what honesty was.
$endgroup$
– J.Moh
Apr 14 at 15:35
$begingroup$
I agree! I found refuge in math and programming since I could sense for the first time what honesty was.
$endgroup$
– J.Moh
Apr 14 at 15:35
$begingroup$
@user21820 I did
$endgroup$
– J.Moh
Apr 14 at 15:36
$begingroup$
@user21820 I did
$endgroup$
– J.Moh
Apr 14 at 15:36
|
show 2 more comments
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3187198%2fwhat-is-the-domain-of-the-function-fx-sqrt3x3-x%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
It is $$x^3-xgeq 0$$
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:39
$begingroup$
I think it's better $D(f)=mathbb R$, but if $g(x)=(x^3-x)^frac13$ so $D(g)=x^3-x>0.$ All these a definition only.
$endgroup$
– Michael Rozenberg
Apr 14 at 9:42
$begingroup$
@Dr.SonnhardGraubner can you explain why?
$endgroup$
– J.Moh
Apr 14 at 9:46
$begingroup$
$$g(0)=0$$ dear Michael.
$endgroup$
– Dr. Sonnhard Graubner
Apr 14 at 9:55
$begingroup$
Are you quite sure it wasn't $sqrtx^3-x$? Because the domain of $sqrt[3]x^3 -x$ is $Bbb R$.
$endgroup$
– TonyK
Apr 14 at 18:21