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whoareyou

Wed Sep 12, 2012 9:43 pm


Inverse of a Function

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Could someone please explain guide me in the right direction as to how to find the inverse of this function?
http://i.imgur.com/JQKGK.png


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Aange10

Thu Sep 13, 2012 8:09 am


RE:Inverse of a Function

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

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


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whoareyou

Thu Sep 13, 2012 8:10 am


RE:Inverse of a Function

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


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Zren

Thu Sep 13, 2012 1:33 pm


RE:Inverse of a Function

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

http://upload.wikimedia.org/math/9/c/7/9c74b71126c6bb1f4d6b865019a2735e.png

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

http://www.purplemath.com/modules/exponent/exp02.gif

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)


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bl0ckeduser

Fri Sep 14, 2012 8:37 am


Re: Inverse of a Function

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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


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Zren

Fri Sep 14, 2012 11:45 am


RE:Inverse of a Function

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

Basically it stated that:

x^-y = 1/x^y