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**aisha00****Member**- Registered: 2010-12-10
- Posts: 17

Find the inverse of the following:-

1)f(x)= (e^x)-(e^-x)/2

The first step I did is to interchange the x and y, then i moved the 2

2x=(e^y)-(e^-y)

Then i find a common factor

2x=e^-y(e^2y-1)

I dunno wht to do after this! The answer for the question is ln(x+√x^2+1)

Thanx

*Last edited by aisha00 (2011-01-09 00:17:52)*

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

You don't need to do much.

the given function is

hence the inverse is , which is

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**aisha00****Member**- Registered: 2010-12-10
- Posts: 17

Um I need to find th inverse using the function given above!

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

you mean, you want to prove arcsinh(x) = ln[ x + sqrt(x^2 + 1)] ?

it's answered here -

http://answers.yahoo.com/question/index?qid=20080810012626AAupFhq

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi aisha00;

aisha wrote:

f(x)= (e^x)-(e^-x)/2

The first thing that you have done is format this wrong. What you have said is this:

But it appears you want this:

Be careful use parentheses liberally. You should have written:

f(x)= ((e^x)-(e^-x))/2

gAr, has pointed you to the right page but we can simplify that idea somewhat. We do not need to use any trig functions.

Say u = e^x

Solve like any other quadratic. There are 2 answers you need only one.

Remember u = e^x.

Change x to y for your problem.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**aisha00****Member**- Registered: 2010-12-10
- Posts: 17

Thanx guys. bobbym u truly are a genius! If u dont mind me asking r u a student?

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

aisha00 wrote:

Thanx guys. bobbym u truly are a genius!

Nope I am not a genius. I am just a guy. I just cleaned up the other guys work, he is a genius.

aisha00 wrote:

If u dont mind me asking r u a student?

This is so corny and pompous, I just have to say it.

The greatest master is but a student.

Good quote huh? I know what you meant, I am kidding. I used to be a student, a horrible one. Disgraced my family!

Are you a student?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**aisha00****Member**- Registered: 2010-12-10
- Posts: 17

Um sorry but I dont get wht u did after u got the quadratic equation u=(√y^2+1)+y! I mean the last 3 steps. Cud u please explain!

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**aisha00****Member**- Registered: 2010-12-10
- Posts: 17

Lol, "This is so corny and pompous, I just have to say it" That made me think u were lyk a 50 year old guy whu had nuthing to do so he was spending time on math forums and just got pissed cuz of my "vorny" question!:P

Yup. I'm a student, and lyk u can see a pretty horrible one :$

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

I feel more like a 150. The guys in the white jackets prop me up in a chair in front of the monitor everyday and do not remove me for 18 - 20 hours. If I do not answer questions they do not feed me. Sometimes they beat the math out of me. Sometimes they use a cattle prod. Is that legal?

Vorny?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**4DLiVing****Member**- Registered: 2011-01-08
- Posts: 22

aisha...

use the quadratic formula for u^2 - 2yu - 1 = 0. Make sure you use a = 1, b = -2y and c = -1 when you substitute.

You will see that y + sqrt(y^2 + 1) comes out as one of the solutions for u, hence

u = y + sqrt(y^2 + 1)

when you substitute e^x back in for u, you then have to take the ln of each side which will:

convert e^x to x on the left and create ln(y + sqrt(y^2 + 1)) on the right.

Then simply switch the x and the y to find the inverse since that has not been done yet, and you have the problem in the form that you want now.

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