How do you find the inverse of #f(x)=ln (3-2x)+3#?

1 Answer
Nov 22, 2015

Inverse is #f^-1(x) = 3/2 - (e^(x-3))/2#

Explanation:

Make #x# the subject in this equation #y= ln(3-2x) + 3#

Step 1) # y-3 = ln(3-2x)#

Step 2) Make exponential expression on both sides to get rid of #ln# so #e^(y-3) = 3-2x#

Step 3) The final form #x= 3/2 - (e^(y-3))/2#

Step 4) Final step replace x by #f^-1 (x)# and #y# by #x#.

Hope that helps,
Cheers.