Inverse of a Function

[whoareyou]

Could someone please explain guide me in the right direction as to how to find the inverse of this function?

[Aange10]

if y = 1/2 (e^x - e^-x) then the inverse is switching the x and y.

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

[whoareyou]

Yeah I got that much, but how would you then isolate for y?

[Zren]

Found this. No idea how they got from a -> b though.



Edit: Ah. Totally forgot about what negative exponents actually represent.



So essentially they write it as:

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

Which they factor out:

(1/2)(1/e^x)((e^x/(1/e^x)) - 1)
(1/2)(1/e^x)((e^x * e^x) - 1)
(1/2)(1/e^x)(e^2x - 1)

[bl0ckeduser]

I have no idea how to help you with this problem, but in light of Zren's saying the function is the same as sinh, maybe this page, which deals with the inverse of sinh, will help.

http://en.wikipedia.org/wiki/Inverse_hyperbolic_function

[Zren]

Ah. Looks like the hotlinked image is down.
http://www.purplemath.com/modules/simpexpo2.htm

Basically it stated that:

x^-y = 1/x^y