Jacobian question - 
I am stuck on a question in my calc III class which is shown above (part a). I completely understand how to find the Jacobian; however I don't understand why the relationship shown is true. How do I find the inverse transformation?
In terms of the Jacobian, I got $$J = \frac{1}{2u}$$.
Thanks for your time. 

Hint: To find J(u, v) you wrote x and y in terms of u and v in preparation to do the differentiation. 
For the inverse you first need to figure out how to express u and v in terms of x any y. 
