Inverse of a function

[elindow]

Here is the function:

y = (1 + e to the x power) / (1 - e to the x power)

What is this functions inverse?? and how do you work this problem??

 

[Gene]

You just swap the x and ys then solve for y
y = (1 + e^x) / (1 - e^x)
x = (1 + e^y) / (1 - e^y)
To simplyfy the writing (and the way it looks) substitute
e^y = z
and solve for z
x=(1+z)/(1-z)
You should be able to solve that for
z = (x-1)/(x+1)
Then un-sub
e^y =(x-1)/(x+1)
Take the ln of both sides
y = ln((x-1)/(x+1))

 

[elindow]

2 Questions....

1) how do you type the powers on here?

2) in the denominator if you solve x = 1+z you get z= -x+1 or an I just too tired to see straight?

 

[Gene]

I used
^{then the exponent followed by}
to end it.

You have to uncheck "Disable HTML in this post" if you have it checked.
You can also use sub instead of sup for a subscript.
If the exponent is a 2 or 3 you can use Alt & 2 or Alt & 3 on most computers.
You can check it out by clicking PREVIEW to see if it looks right.
Hope this makes sense.

 

[elindow]

testing ............. y = (1+e^x)/(1-e^x)Q_o

Ok got it to work good

 

[mathmike]

2) in the denominator if you solve x = 1+z you get z= -x+1 or an I just too tired to see straight?

you're, Gene is right - show what you've got, though.

 

[Gene]

I did
x=(1+z)/(1-z)
(x-xz)=(1+z)
x-1=z+xz
x-1=z(1+x)
(x-1)/(x+1)=z

 

[elindow]

I figured it out.....thanks I was just not seeing straight....I am going to bed now and I can get the other problem in class.

Thanks
Erik