Question

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

Answer 1

what does "pattern for the inverse" mean?

Answer 2

we can actually find the inverse if you like

Answer 3

I'm assuming it just means a forumla.

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

we can work through it completely if you like

Answer 8

Um... Yes, please.

Answer 9

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

Answer 10

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

Answer 11

Ohhhhhhhh, okay! Thank you~!