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

1 Answer
George C.
Oct 24, 2015

Let #y = f(x)# and solve for #x# in terms of #y# to find:

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

Explanation:

Let #y = f(x) = (x-2)/(x+2) = ((x+2)-4)/(x+2) = 1-4/(x+2)#

Then #1-y = 4/(x+2)#

Hence #x+2 = 4/(1-y)#

So #x = 4/(1-y)-2 = (4-2(1-y))/(1-y) = (2y+2)/(1-y) = (2(y+1))/(1-y)#

So #f^(-1)(y) = (2(y+1))/(1-y)#

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