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## #1 2011-01-09 00:17:34

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

### Helpi with finding the inverse of an exponential function

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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## #2 2011-01-09 01:55:01

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

### Re: Helpi with finding the inverse of an exponential function

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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## #3 2011-01-09 03:01:50

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

### Re: Helpi with finding the inverse of an exponential function

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

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## #4 2011-01-09 04:09:01

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

### Re: Helpi with finding the inverse of an exponential function

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

"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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## #5 2011-01-09 04:59:48

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

### Re: Helpi with finding the inverse of an exponential function

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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## #6 2011-01-09 06:19:34

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

### Re: Helpi with finding the inverse of an exponential function

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

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## #7 2011-01-09 06:24:43

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

### Re: Helpi with finding the inverse of an exponential function

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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## #8 2011-01-09 06:32:42

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

### Re: Helpi with finding the inverse of an exponential function

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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## #9 2011-01-09 06:35:14

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

### Re: Helpi with finding the inverse of an exponential function

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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## #10 2011-01-09 06:47:01

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

### Re: Helpi with finding the inverse of an exponential function

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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## #11 2011-01-09 06:57:45

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

### Re: Helpi with finding the inverse of an exponential function

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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