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)#