Find and sketch the domain of the function

Question

Hi, I need to know if Im right. Function is : 

 

f(x,y)= (ln(2-x))/(1-x² -y² ) so x <2 and x² +y² <1 

 

Graphing this, I shaded everything less than x=2 and shaded the circle. 

Answer 1

I think that the circle should be made with dashes to convey the idea that only its INTERIOR contains points in the domain. Don't worry about the requirement that x < 2 because the limitations |x| < 1 and |y| < 1 (associated with the circle) already guarantee that the argument of the natural logarithm will be OK in every instance.