How do you find the inverse of #f^-1(x)= -2 - 1/(x-1)#?

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Answer 1 · 2016-06-04T22:39:21

You can consider your #f^(-1)(x)# as a new variable #y#.
Then you write

#y=-2-1/(x-1)#

now, to invert it, you want to obtain #x# as function of #y#.

#y=-2-1/(x-1)#

#y+2=-1/(x-1)#

#-(y+2)=1/(x-1)#

#-1/(y+2)=x-1#

#1-1/(y+2)=x#

This is your inverse function.