exponential problem (1 Viewer)

[underthesun]

Last year, during the HSC, I had to sit down for the extension 1 maths, and there was this question:

Find the inverse function of:

y = e^x + e^(-x)

for x less or equal to zero.

I had to repeat maths because my hsc mark was only 86 (despite the 96 exam mark), since I bludged too much and got almost the bottom rank at the school, and I guess now's the proving time. But I can't even seem to work this out.. anybody?

 

[spice girl]

Ahh this one

it took me a while too...

anyhow:

y = (e^2x + 1)/e^x
y*e^x = e^2x + 1
(e^x)^2 - y*e^x + 1 = 0

then using quadratic formula, we find e^x

then we log both sides to express x in terms of y.

 

[underthesun]

hey -- thanks a lot
feel free to sign my "nearly the best guestbook on earth" now </shameless promotion>

 

[ReaveR]

Waaah...I'm lost!
How can there be an inverse function for this when there are two x-values for every y? It fails the horizontal line test!!

 

[spice girl]

Add the restriction x >= 0 and you should be fine