Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Find Domain of A

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

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Find Domain of A

That looks right to me.

B

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Domain of A

That looks right to me.

B

Very good. Happy to be right.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Re: Find Domain of A

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)

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Domain of A

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 mathxyz (2024-03-17 01:33:13)

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Domain of A

That looks right to me.

B

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Find Domain of A

hi KerimF,

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

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Re: Find Domain of A

"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.

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Domain of A

"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

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Re: Find Domain of A

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

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Domain of A

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

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Re: Find Domain of A

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.

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Domain of A

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

Member

Registered: 2023-09-19

Posts: 253

Re: Find Domain of A

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Domain of A

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]