Find the inverse function f^-1 (x) if f(x) = (x+1)/(2x-5)?

We'll interchange x and y and we'll
have:

x =  (y+1)/(2y-5)

Now,
we'll multiply both sides by 2y - 5:

x(2y - 5) = y +
1

We'll remove the
brackets:

2xy - 5x = y +
1

We'll keep all the terms in y to the left side, the rest
of term being shifted to the right side.

2xy - y = 5x +
1

We'll factorize by y to the left
side:

y(2x - 1) =5x + 1

We'll
divide by 2x - 1

y = (5x + 1)/(2x -
1)

The inverse function is: f^-1(x) = (5x +
1)/(2x - 1).