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

##### 1 Answer

Dec 13, 2015

#### Explanation:

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

Switch

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

Multiply both side by

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

Distribute

#xy+2x = y-2#

Bring all "y" term to one side and factor

#2x+2 = y-xy#

Factor, and solve for

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

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

Replace

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