Find a formula for the inverse of the function, f(x)= 8-3/x^2, x> 0. explain if you can.

Starting with f(x)= 8-3/x^2, x>0,
1.  Replace "f(x)" by "y:"  y= 8-3/x^2
2.  Interchange x and y:  x = 8-3/y^2
3.  Solve this equation for y:    3/(y^2) = 8 - x, or (y^2)/3 = 1/(8-x)

3a.     This becomes y^2 = 3/(8-x).  Solving for y results in two values:
                 y=sqrt(3/[8-x]) and y= -sqrt(3/[8-x] 

4.  Determine the domain of this inverse function:
      a.  Note that div. by zero is not allowed, so x must be less than 8
      b.  Another reason that x must be less than 8 is that the radicand 3/[8-x]         MUST be positive.