How do you find #f ^-1(x)# given #f(x) = (x+1)/(x+2)# when x ≠ -2?

1 Answer
Jun 15, 2016

#f^-1(x) = (1-2*x)/(x-1)#

Explanation:

First : we will replace all #x# by #y# and the #y# by #x#

Here we have :
#x=(y+1)/(y+2)#

Second: solve for #y#

# x*(y+2)=y+1#
#x*y +2*x = y+1#

Arrange all #y# in one side:

#x*y - y= 1-2*x#

Taking #y# as common factor we have:
#y*(x-1)=1-2*x#
#y=(1-2*x)/(x-1)#

Therefore,
#f^-1(x)=(1-2*x)/(x-1)#