The function f(x)=(2x+1)/(2x-1) has an inverse. Which is the inverse?

First, we'll write:

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

Now, we'll solve this equation 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 = 1-2y

We'll factorize:

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

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

Now, we'll interchange x and y:

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

So, the inverse function is:

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