Find Domain of A

nycguitarguy · 2024-03-16 01:29:25

Given A(x) = 4x•sqrt{1 - x^2}, find the domain of A.

I believe to find the domain, I must set the radicand 1 - x^2 to be greater rhan or equal to 0.

Let => represent greater than or equa to.

1 - x^2 => 0

-x^2 => -1

Dividing both sides by -1, I get this:

x^2 <= 1, the symbol <= represents less than or equal to.

sqrt{x^2} <= sqrt{1}

x <= 1

Domain = all real numbers between -1 & 1 INCLUDING -1 & 1.

We can say it this way:

Domain = [-1, 1]

You say?

Bob · 2024-03-16 02:03:59

That looks right to me.

B

nycguitarguy · 2024-03-16 12:00:39

Bob wrote:

That looks right to me.
B

Very good. Happy to be right.

KerimF · 2024-03-17 00:51:32

Hi Bob,
It seems that that 'range and 'domain' could be applied both on the variable or the function.
I thought, so I may be wrong, that 'domain' is for the variable only and 'range' is for the function only.
Please clarify this point.
Thank you.
Kerim

Last edited by KerimF (2024-03-17 00:52:57)

nycguitarguy · 2024-03-17 01:19:20

KerimF wrote:

Hi Bob,
It seems that that 'range and 'domain' could be applied both on the variable or the function.
I thought, so I may be wrong, that 'domain' is for the variable only and 'range' is for the function only.
Please clarify this point.
Thank you.
Kerim

Last edited by nycguitarguy (2024-03-17 01:33:13)

nycguitarguy · 2024-03-17 01:20:34

Bob wrote:

That looks right to me.
B

Last edited by nycguitarguy (2024-03-17 01:32:51)

Bob · 2024-03-17 01:28:06

hi KerimF,

I'm using the Wolfram Alpha definitions: domain for the independent variable and range for the dependent one.

Bob

KerimF · 2024-03-17 02:51:47

"Given A(x) = 4x•sqrt{1 - x^2}, find the 'domain' of A."

A(x) is supposed to be a dependent variable, so I expected to read... find the 'range' of A.

nycguitarguy · 2024-03-17 11:55:15

KerimF wrote:

"Given A(x) = 4x•sqrt{1 - x^2}, find the 'domain' of A."
A(x) is supposed to be a dependent variable, so I expected to read... find the 'range' of A.

I type my questions as stated in the textbooks.

KerimF · 2024-03-17 12:22:50

What confuses me is how one gives a result as 'a range' and as 'a domain'!

nycguitarguy · 2024-03-17 19:43:09

KerimF wrote:

What confuses me is how one gives a result as 'a range' and as 'a domain'!

I don't understand your confusion.

Find the domain is not the same as find the range.
I type all questions as stated in the textbooks.

KerimF · 2024-03-17 22:02:17

FelizNYC wrote:

KerimF wrote:
What confuses me is how one gives a result as 'a range' and as 'a domain'!
I don't understand your confusion.
Find the domain is not the same as find the range.
I type all questions as stated in the textbooks.

Sorry if I gave you the impressing that I am arguing with you or else. Please note that I believe whatever you say.

I just knew things in math that are somehow different from what I see here sometimes. That is all.

So, when in doubt, I believe that Bob, for example, can help clarifying the math definitions of interest, as they are followed on his side and yours.

On my side, I have no reason not to accept anything you say. After all, at work, I don't follow any definition. I just solve math problems and get numerical/practical results.

nycguitarguy · 2024-03-18 01:39:53

KerimF wrote:

FelizNYC wrote:
KerimF wrote:
What confuses me is how one gives a result as 'a range' and as 'a domain'!
I don't understand your confusion.
Find the domain is not the same as find the range.
I type all questions as stated in the textbooks.
Sorry if I gave you the impressing that I am arguing with you or else. Please note that I believe whatever you say.
I just knew things in math that are somehow different from what I see here sometimes. That is all.
So, when in doubt, I believe that Bob, for example, can help clarifying the math definitions of interest, as they are followed on his side and yours.
On my side, I have no reason not to accept anything you say. After all, at work, I don't follow any definition. I just solve math problems and get numerical/practical results.

Thank you for the feedback.

amnkb · 2024-03-18 09:53:30

FelizNYC wrote:

Given A(x) = 4x•sqrt{1 - x^2}, find the domain of A.

Theres a way to do this so you dont have to try to go from 'x<=1' to '-1<=x<=1'

This gives you two sol'ns: x=1, x=-1

Also you know shape of quadratics like y=x^2-1:
<=0 between sol'ns (when its positive like this)

This lets you go to

nycguitarguy · 2024-03-18 19:54:48

amnkb wrote:

FelizNYC wrote:
Given A(x) = 4x•sqrt{1 - x^2}, find the domain of A.
Theres a way to do this so you dont have to try to go from 'x<=1' to '-1<=x<=1'
This gives you two sol'ns: x=1, x=-1
Also you know shape of quadratics like y=x^2-1:
<=0 between sol'ns (when its positive like this)
This lets you go to

Domain = [-1, 1]

Math Is Fun Forum

#1 2024-03-16 01:29:25

Find Domain of A

#2 2024-03-16 02:03:59

Re: Find Domain of A

#3 2024-03-16 12:00:39

Re: Find Domain of A

#4 2024-03-17 00:51:32

Re: Find Domain of A

#5 2024-03-17 01:19:20

Re: Find Domain of A

#6 2024-03-17 01:20:34

Re: Find Domain of A

#7 2024-03-17 01:28:06

Re: Find Domain of A

#8 2024-03-17 02:51:47

Re: Find Domain of A

#9 2024-03-17 11:55:15

Re: Find Domain of A

#10 2024-03-17 12:22:50

Re: Find Domain of A

#11 2024-03-17 19:43:09

Re: Find Domain of A

#12 2024-03-17 22:02:17

Re: Find Domain of A

#13 2024-03-18 01:39:53

Re: Find Domain of A

#14 2024-03-18 09:53:30

Re: Find Domain of A

#15 2024-03-18 19:54:48

Re: Find Domain of A

Board footer