What is the simplified inverse of f(x)=(x-2)/(x+2)?

Question

What is the simplified inverse of f(x)=(x-2)/(x+2)?

Answer 1

to create the inverse, you simply swap all the x's with y's, and y's with x's

you get x = (y - 2)/(y + 2), which cannot be simplified further

Answer 2

You already asked another question like this. I answered one of your other same math questions. I gave you the answer and showed you tips and definitions. You should study that carefully, and look up inverses, converses, and contrapositives online if you can't understand it on Answers. Don't expect everyone to do your math homework for you. You'll never learn unless you try it yourself.

Answer 3

Put y = f(x), i.e. x = g(y) where g is the inverse of f

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

=>

y(x+2) = x-2

=>

yx + 2y = x - 2

=>

yx - x = -2 - 2y

=>

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

=>

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

=>

g(y) = 2(1+y)/(1-y)

So g(x) = 2(1+x)/(1-x)

Try it: if x = 4 then f(x) = 2/6 = 1/3

Put x=1/3 into g(x) = 2(1+1/3)/(1-1/3) = 2*(4/3)/(2/3) = 4