Q1: Given the function f: (A U B) to C, which of the following is always true?

The choice is f(A U B)=f(A) U f(B).

Why? Is there any theorem about it?

Q2: The moment with respect to yz plane of the volume in the first octant bounded by f(x,y,z) and g(x,y,z), and balabalabala....

My question is why the answer is triple integral on volume v [(x) dxdydz], why is there an x in the integral?

Q3: Given x^2 *z-2y*z^2+xy=0, find dx/dz at (1,1,1).

I know first I need to caculate df/dx and df/dz, and then I use dx/dz=(df/dz)/(df/dx), but the answer shows that dx/dz= -(df/dz)/(df/dx), why there is a negative one there? Feeling puzzle....

Thanks for your replies.