Question

find the inverse of f(x)= (3^x)/(2-3^x)

Answer 1

the x powers are the part that is confusing me, I know I have to solve for x and then switch the x and y... but I cant get to that poing

Answer 2

first..change f(x) into y
\[y = \frac{3^x}{2 - 3^x}\]
cross multiply
\[\implies y(2 - 3^x) = 3^x\]
distribute
\[\implies 2y - y3^x = 3^x\]
put the x terms on one side
\[\implies 2y = 3^x + y3^x\]
factor out
\[2 = 3^x(1 + y)\]
divide both sides by 1 + y
\[\frac{2}{1+y} = 3^x\]
change to log form
\[\log_3 \left (\frac{2}{1+y}\right) = x\]
does that help?

Answer 3

@cmgeorgia you there?

Answer 4

yes, I was reviewing the problem. Thank you so much! One thing to clarify, shouldn't it be 2y/ 1+y)?

Answer 5

ahh yes..good observation :D

Answer 6

okay just making sure! Thanks again!

Answer 7

welcome