Determine the inverse of y = (2x - 1)/(2x + 1)

We'll solve this equation y=(2x-1)/(2x+1) for x,
multiplying both sides by (2x+1):

2xy+y =
(2x-1)

We'll move all terms containing x, to the left side
and all terms in y, to the right side:

2xy-2x =
-1-y

We'll factorizeby
2x:

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

We'll
divide by 2(y-1)

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

Now, we'll interchange x and
y:

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

So, the
inverse function is:

[f(x)]^(-1) =
-(1+x)/2(x-1)