Category: Test #1 Solutions (Page 1 of 2)

Version B, Question 9

Let f(x)=(x-1)/(x+2). Determine whether f(x) is invertible. If f(x) is invertible, find its inverse. If f(x) is not invertible, explain why not.

First replace f(x) with y.

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

Next switch x with y.

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

Multiply both sides by (y+2)

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

Distribute

xy+2x=(y-1)

Rearrange the terms.

xy-y=-2x-1

Factor out y

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

Divide both sides by (x-1)

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

Replace y with f^-1(x)

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

f(x) is invertible.