SOLUTION: Find the inverse function of f f(x) = x-2/x+2 y = x-2/x+2 = (x+2)y = x-2 yx + 2y = x-2 yx-x = -2y-2 x(y-1) = -2y-2 x = 2(y-1)/y-1 f^-1(x) = 2x-2/y-1 Thank you for all

Algebra ->  Functions -> SOLUTION: Find the inverse function of f f(x) = x-2/x+2 y = x-2/x+2 = (x+2)y = x-2 yx + 2y = x-2 yx-x = -2y-2 x(y-1) = -2y-2 x = 2(y-1)/y-1 f^-1(x) = 2x-2/y-1 Thank you for all      Log On


   

Question 45521This question is from textbook College Algebra
: Find the inverse function of f
f(x) = x-2/x+2
y = x-2/x+2 = (x+2)y = x-2
yx + 2y = x-2
yx-x = -2y-2
x(y-1) = -2y-2
x = 2(y-1)/y-1
f^-1(x) = 2x-2/y-1
Thank you for all your help! This question is from textbook College Algebra

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x-2/x+2
y=(x-2)/(x+2)
Interchange x and y to get:
x=(y-2)/(y+2)
Solve for y as follows:
x(y+2)=y-2
xy+2x = y-2
y-xy=2x+2
y(1-x)=2x+2
y= (2x+2)/(1-x), x not equal to 1
This is the inverse.
cheers,
Stan H.