Hi ,

Show that the inverse of a linear fraction function is always a linear fraction function (except where it is not defined).

Let, f(x) = (a+bx)/(c+dx) be the said linear fraction function.

Let at some x it attains value y, so,

                 (a+bx)/(c+dx) = y

                => a + bx - cy - dxy = 0

                => a - cy + x (b - dy) = 0

                => x = (cy-a)/(b-dy).

Which is again a linear fraction function defined in R except

                 at x = -c/d and y = b/d

and inverse of the given function is, y = (cx-a)/(b-dx).