Find a pattern for the inverse of f(x)if f(x)=(a^x + 1)/(a^x - 1)
((plsplspls help))

Question

Find a pattern for the inverse of f(x)if f(x)=(a^x + 1)/(a^x - 1)
((plsplspls help))

anonymous · Answer

what does "pattern for the inverse" mean?

anonymous · Answer

we can actually find the inverse if you like

anonymous · Answer

I'm assuming it just means a forumla.

anonymous · Answer

Yes, that'd be nice. I'm sorry about that late reply, my connection's being wonky. I can do inverses alright, but I've never had to do one with the variable as an exponent.

anonymous · Answer

do it the same way, but the last step will be to take the log

anonymous · Answer

you need the algebra?  the second to last step will be 
$$a^y=\frac{x+1}{x-1}$$

anonymous · Answer

we can work through it completely if you like

anonymous · Answer

Um... Yes, please.

anonymous · Answer

$$x=\frac{a^y+1}{a^y-1}$$
$$xa^y-x=a^y+1\
xa^y-a^y=x+1\
a^y(x-1)=x+1\
a^y=\frac{x+1}{x-1}$$

anonymous · Answer

and so 
$$y=\log_a(\frac{x+1}{x-1})$$

anonymous · Answer

Ohhhhhhhh, okay! Thank you~!