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.