Question

f(x) = (1+e^x)/(1-e^x)
Find the inverse function.

Answer 1

A function does this\[x \rightarrow (1+e^x)/(1-e^x)\]The inverse of that function does this\[(1+e^x)/(1-e^x) \rightarrow x\]
So in f(x) = (1+e^x)/(1-e^x), just replace all the x's by f(x)'s and f(x)'s by x's and rearrange.

Answer 2

\[x = \frac{(1+e^{f(x)})}{(1-e^{f(x)})}\]
\[x-xe^{f(x)}=1+e^{f(x)}\]
\[x-1=e^{f(x)}(1+x)\]
\[\frac{x-1}{(1+x)}=e^{f(x)}\]
\[\large e^{ln\frac{x-1}{(1+x)}}=e^{f(x)}\]
\[\large {ln\frac{x-1}{(1+x)}}={f(x)}\]

Answer 3

Are you familiar with logs? \[\ln=\log_e\]

Answer 4

Kind of, not really that familiar with the whole ln = log e.

Answer 5

\[a=b^c\]
\[c=log_b(a)=\text{'the thing that you have to raise b to the power of to get a'}\]So obviously\[\large b^{\log_b(a)}=a\]Same thing here, just we are using not b, but e, and not a, but (x-1)/(x+1)

Answer 6

http://www.youtube.com/watch?v=mQTWzLpCcW0

Answer 7

Ooooh okay thanks! I will have to watch that video right now.

Answer 8

Basically it's a condensed way to write a relatively simple thing. Got to go, bump question if more help needed later.