The function is

f is increasing over its entire domain, . To verify this, note that is positive on the domain of f. So, f is strictly monotonic and it must have an inverse function. To find an equation for the inverse function, let y = f(x) and solve for x in terms of y.

           (Let y = f(x))

           (Multiply each side by x)

           (Subtract x from each side)

        (Take out common term x)

        (Divide each side by )

           (Interchange x and y)

   (Replace y by )

Therefore the inverse function of f is .