How do you find the inverse of #y = (x+3)/(x-2)# and is it a function?

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Answer 1 · 2017-12-24T13:27:20

Inverse of #y=(x+3)/(x-2)# is #y=(2x+3)/(x-1)#

As #y=(x+3)/(x-2)#

#xy-2y=x+3#

or #xy-x=2y+3#

or #x(y-1)=2y+3#

or #x=(2y+3)/(y-1)#

Hence inverse of #y=(x+3)/(x-2)# is #y=(2x+3)/(x-1)#

Observe that each of the function is a reflection of the other in the line #x=y#.

graph{(y-(x+3)/(x-2))(y-(2x+3)/(x-1))(x-y)=0 [-10, 10, -5, 5]}