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

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Answer 1 · 2015-06-29T21:02:08

Find the inverse of #g(x)# by simplifying it to have one occurrence of #x# then rearranging to express #x# in terms of #g(x)#

#g^-1(y) = 3+5/(y-1)#

Let #y = g(x)#

Then

#y = (x+2)/(x-3) = (x-3+5)/(x-3) = 1+5/(x-3)#

Subtract #1# from both ends to get:

#y - 1 = 5/(x-3)#

Multiply both sides by #(x-3)# to get:

#(y-1)(x-3) = 5#

Divide both sides by #(y-1)# to get:

#x - 3 = 5/(y-1)#

Add #3# to both sides to get:

#x = 3 + 5/(y-1)#

So #g^-1(y) = 3+5/(y-1)#