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

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Answer 1 · 2015-12-13T00:35:37

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

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

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

Switch #x# for #y# and #y# for #x#

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

Multiply both side by #y+2#

#(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 #y#

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

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

Replace #y# with inverse notation #f^(-1)(x)#

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